The geometry and topology of Coxeter groups
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[1] B. Rémy,et al. Simplicité abstraite des groupes de Kac–Moody non affines , 2006 .
[2] S. Eilenberg,et al. On the Lusternik-Schnirelmann Category of Abstract Groups , 1957 .
[3] Robert D. Edwards,et al. The Topology of Manifolds and Cell-Like Maps , 2010 .
[4] K. S. Brown. Homological criteria for finiteness , 1975 .
[5] Ruth Charney. STRICT HYPERBOLIZATION , 2003 .
[6] Robert Schrader,et al. On the curvature of piecewise flat spaces , 1984 .
[7] John Milnor,et al. A note on curvature and fundamental group , 1968 .
[8] A. Reid,et al. Infinite Coxeter groups are virtually indicarle , 1998, Proceedings of the Edinburgh Mathematical Society.
[9] Dongwen Qi. On Irreducible, Infinite, Non-affine Coxeter Groups , 2006, math/0603670.
[10] F. Farrell,et al. On Novikov's Conjecture for Non-Positively Curved Manifolds, I , 1981 .
[11] H. Busemann. Spaces with non-positive curvature , 1948 .
[12] Igor Nikolaev,et al. Generalized Riemannian spaces , 1986 .
[13] R. Varga,et al. Proof of Theorem 4 , 1983 .
[14] J. Crisp. Symmetrical Subgroups of Artin Groups , 2000 .
[15] Tadeusz Januszkiewicz,et al. Cohomology of buildings and of their automorphism groups , 2002 .
[16] William J. Floyd,et al. Symmetries of planar growth functions , 1988 .
[17] Huai-Dong Cao,et al. A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow , 2006 .
[18] Ki Hang Kim,et al. Homology of certain algebras defined by graphs , 1980 .
[19] Local homology properties of boundaries of groups. , 1996 .
[20] Ennis Rosas,et al. RIGIDITY THEOREMS FOR RIGHT ANGLED REFLECTION GROUPS , 1988 .
[21] E. Witt,et al. Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe , 1941 .
[22] Ruth Charney,et al. The (,1)-problem for hyperplane complements associated to infinite reflection groups , 1995 .
[23] Jeff Cheeger,et al. L2-Cohomology and group cohomology , 1986 .
[24] È. Vinberg,et al. Some linear groups virtually having a free quotient. , 2000 .
[25] A. Kaul. Rigidity for a class of Coxeter groups , 2000 .
[26] Geodesics in piecewise linear manifolds , 1976 .
[27] N. Meyers,et al. H = W. , 1964, Proceedings of the National Academy of Sciences of the United States of America.
[28] J. W. Cannon,et al. Shrinking cell-like decompositions of manifolds. Codimension three , 1979 .
[29] John McCleary,et al. User's Guide to Spectral Sequences , 1985 .
[30] Gabor Moussong,et al. Hyperbolic Coxeter groups , 1988 .
[31] H. Minkowski,et al. Zur Theorie der positiven quadratischen Formen. , 1887 .
[32] T. Januszkiewicz,et al. Hyperbolization of polyhedra , 1991 .
[33] R. Lashof,et al. Problems in Differential and Algebraic Topology. Seattle Conference, 1963 , 1965 .
[34] Homological algebra of Novikov-Shubin invariants and morse inequalities , 1996, dg-ga/9606013.
[35] William P. Thurston,et al. Hyperbolic Structures on 3-manifolds, I: Deformation of acylindrical manifolds , 1986, math/9801019.
[36] Michael Davis. Some aspherical manifolds , 1987 .
[37] B. Nucinkis,et al. Some groups of type VF , 2003 .
[38] Luis Paris. Irreducible Coxeter Groups , 2007, Int. J. Algebra Comput..
[39] G. Lusztig. Left cells in weyl groups , 1983 .
[40] Jacques Tits,et al. A Local Approach to Buildings , 1981 .
[41] Daniel E Cohen,et al. Groups of Cohomological Dimension One , 1972 .
[42] S. Weinberger. The Topological Classification of Stratified Spaces , 1995 .
[43] F. Farrell. Poincaré daulity and groups of type (FP) , 1975 .
[44] Allan M. Sinclair,et al. The basic construction , 2008 .
[45] The FAn Conjecture for Coxeter groups , 2005, math/0509439.
[46] Michael W. Davis. The cohomology of a Coxeter group with group ring coefficients , 1998 .
[47] R. Ho. Algebraic Topology , 2022 .
[48] Friedrich Hirzebruch,et al. Groupes et géométries de Coxeter , 2001 .
[49] F. Raymond,et al. Separation and union theorems for generalized manifolds with boundary. , 1960 .
[50] G. Perelman. The entropy formula for the Ricci flow and its geometric applications , 2002, math/0211159.
[51] Nellie Clarke Brown. Trees , 1896, Savage Dreams.
[52] È. Vinberg,et al. Strong Tits alternative for subgroups of Coxeter groups. , 2002 .
[53] P. A. Smith. Transformations of Finite Period. II , 1938 .
[54] Curtis T. McMullen,et al. Coxeter groups, Salem numbers and the Hilbert metric , 2002 .
[55] J. Hausmann,et al. Aspherical manifolds without smooth or PL structure , 1989 .
[56] M. Kreck. The Novikov Conjecture: Geometry and Algebra , 2005 .
[57] Swiatoslaw R. Gal. Real Root Conjecture Fails for Five- and Higher-Dimensional Spheres , 2005, Discret. Comput. Geom..
[58] F. Raymond,et al. Manifolds covered by Euclidean space , 1975 .
[59] É. Ghys,et al. Sur Les Groupes Hyperboliques D'Apres Mikhael Gromov , 1990 .
[60] E. Robertson,et al. Buildings and group amalgamations , 1987 .
[61] Walter Feit,et al. The nonexistence of certain generalized polygons , 1964 .
[62] Mladen Bestvina,et al. The boundary of negatively curved groups , 1991 .
[63] Charles F. Miller,et al. Combinatorial Group Theory , 2002 .
[64] John Stallings,et al. Group Theory and Three-dimensional Manifolds , 1971 .
[65] E C G Sudarshan,et al. Lie Groups and Lie Algebras , 2010 .
[66] H. Hopf. Fundamentalgruppe und zweite Bettische Gruppe , 1941 .
[67] R. Strebel. A remark on subgroups of infinite index in Poincaré duality groups , 1977 .
[68] F. Farrell,et al. A topological analogue of Mostow’s rigidity theorem , 1989 .
[69] R. G. Möller. Groups acting on graphs , 1991 .
[70] Jacek Świa¸tkowski. Trivalent Polygonal Complexes of Nonpositive Curvature and Platonic Symmetry , 1998 .
[71] Mark Ronan,et al. Lectures on Buildings , 1989 .
[72] Ruth Charney,et al. Singular Metrics of Nonpositive Curvature on Branched Covers of Riemannian Manifolds , 1993 .
[73] M. Newman,et al. The Engulfing Theorem for Topological Manifolds , 1966 .
[74] Warren Dicks,et al. Presentations for subgroups of Artin groups , 2012, 1210.6585.
[75] John Stallings,et al. Polyhedral homotopy-spheres , 1960 .
[76] R. Kirby,et al. On the triangulation of manifolds and the Hauptvermutung , 1969 .
[77] B. Mühlherr. The isomorphism problem for Coxeter groups , 2005 .
[78] Ruth Charney,et al. Finite K (π, 1)s for Artin Groups , 1996 .
[79] M. Atiyah. Elliptic operators, discrete groups and von Neumann algebras , 1976 .
[80] J. Munkres. Obstructions to imposing differentiable structures , 1964 .
[81] Finite automorphisms of negatively curved Poincaré duality groups , 2003, math/0302218.
[82] J. Whitehead. Certain theorems about three-dimensional manifolds (i) , 1934 .
[83] D. L. Johnson. Topics in the Theory of Group Presentations: Small cancellation groups , 1980 .
[84] W. Browder. Surgery on Simply-Connected Manifolds , 1972 .
[85] B. Eckmann. Poincaré Duality Groups of Dimension Two are Surface Groups , 1987 .
[86] B. Eckmann,et al. Poincaré duality groups of dimension two , 1980 .
[87] Vinay V. Deodhar. A note on subgroups generated by reflections in Coxeter groups , 1989 .
[88] I. Kaplinskaya. Discrete groups generated by reflections in the faces of symplicial prisms in Lobachevskian spaces , 1974 .
[89] M. Bridson,et al. Complexes of Groups , 1999 .
[90] Ruth Charney,et al. Notes on Locally CAT(l) Spaces , 1995 .
[91] F. Farrell,et al. Topological rigidity for compact non-positively curved manifolds , 1990 .
[92] M. Spivak. A comprehensive introduction to differential geometry , 1979 .
[93] J. Lott,et al. L 2-Topological Invariants of 3-manifolds by , 1995 .
[94] Tadeusz Januszkiewicz,et al. Nonpositive curvature of blow-ups , 1998 .
[95] G. Perelman. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds , 2003, math/0307245.
[96] J. Whitehead. A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY , 1935 .
[97] È. Vinberg,et al. DISCRETE LINEAR GROUPS GENERATED BY REFLECTIONS , 1971 .
[98] Charles F. Miller. Decision Problems for Groups — Survey and Reflections , 1992 .
[99] D. Sullivan. HYPERBOLIC GEOMETRY AND HOMEOMORPHISMS , 1979 .
[100] Ruth Charney,et al. The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. , 1995 .
[101] R. Geoghegan,et al. The fundamental group at infinity , 1996 .
[102] M. Newman,et al. Boundaries of ULC Sets in Euclidean n-Space. , 1948, Proceedings of the National Academy of Sciences of the United States of America.
[103] G. Perelman. Ricci flow with surgery on three-manifolds , 2003, math/0303109.
[104] M. Gromov,et al. Hyperbolic Manifolds, Groups and Actions , 1981 .
[105] Thin buildings , 2005, math/0601005.
[106] Jacques Tits,et al. Buildings of Spherical Type and Finite BN-Pairs , 1974 .
[107] Vanishing theorems and conjectures for the, $\ell ^2$--homology of right-angled Coxeter groups , 2001, math/0102104.
[108] B. Jackson. End invariants of group extensions , 1982 .
[109] M. Bourdon. Immeubles hyperboliques, dimension conforme et rigidité de Mostow , 1997 .
[110] Bijin Hu. Whitehead groups of finite polyhedra with nonpositive curvature , 1993 .
[111] B. Eckmann. Introduction to ℓ2-methods in topology: Reduced ℓ2-homology, harmonic chains, ℓ2-betti numbers , 2000 .
[112] N. Brady,et al. On Algebraic and Geometric Dimensions for Groups with Torsion , 2001 .
[113] M. J. Dunwoody. The accessibility of finitely presented groups , 1985 .
[114] W. Ballmann,et al. Polygonal complexes and combinatorial group theory , 1994 .
[115] J. Meier,et al. The topology at infinity of Coxeter groups and buildings , 2002 .
[116] W. Thurston. Three dimensional manifolds, Kleinian groups and hyperbolic geometry , 1982 .
[117] R. Howlett,et al. Automorphisms of nearly finite Coxeter groups. , 2003 .
[118] W. Lück. L 2 -Invariants of Regular Coverings of Compact Manifolds and CW-Complexes , 2001 .
[119] M. Gromov. Kähler hyperbolicity and $L_2$-Hodge theory , 1991 .
[120] J. Cannon. The combinatorial structure of cocompact discrete hyperbolic groups , 1984 .
[121] László Lovász,et al. The Shapes of Polyhedra , 1990, Math. Oper. Res..
[122] H. Pajot,et al. Rigidity of quasi-isometries for some hyperbolic buildings , 2000 .
[123] M. Bourdon. Sur les immeubles fuchsiens et leur type de quasi-isométrie , 2000, Ergodic Theory and Dynamical Systems.
[124] Michah Sageev,et al. Ends of Group Pairs and Non‐Positively Curved Cube Complexes , 1995 .
[125] On subgroups of Coxeter groups , 2007, 0711.5011.
[126] The Poincaré Conjecture 99 Years Later : A Progress Report , 2022 .
[127] G. Dirac. On rigid circuit graphs , 1961 .
[128] Ravi S. Kulkarni,et al. Regular tessellations of surfaces and (p, q, 2)-triangle groups , 1982 .
[129] Colin Rourke,et al. Block bundles: I , 1968 .
[130] Michael H. Freedman,et al. The topology of four-dimensional manifolds , 1982 .
[131] Topology of homology manifolds , 1993, math/9304210.
[132] T. Dieck. Orbittypen und äquivariante Homologie. I , 1972 .
[133] Marvin Mudrick,et al. Here They Are , 1972 .
[134] Michael W. Davis. Groups Generated by reflections and aspherical manifolds not covered by Euclidean space , 1983 .
[135] John Stallings,et al. On Torsion-Free Groups with Infinitely Many Ends , 1968 .
[136] A. Lubotzky. Free quotients and the first betti number of some hyperbolic manifolds , 1996 .
[137] Folke Lannér. On complexes with transitive groups of automorphisms , 1950 .
[138] Michael W. Davis,et al. NOTES ON NONPOSITIVELY CURVED POLYHEDRA , 2004 .
[139] A. Blumberg. BASIC TOPOLOGY , 2002 .
[140] Michael W. Davis,et al. When is a Coxeter System Determined by its Coxeter Group? , 2000 .
[141] D. Kazhdan,et al. Representations of Coxeter groups and Hecke algebras , 1979 .
[142] R. Geroch. Positive sectional curvatures does not imply positive Gauss-Bonnet integrand , 1976 .
[143] H. van der Lek,et al. The homotopy type of complex hyperplane complements , 1983 .
[144] Constantin Gonciulea. Infinite Coxeter groups virtually surject onto Z , 1997 .
[145] T. Januszkiewicz,et al. Convex polytopes, Coxeter orbifolds and torus actions , 1991 .
[146] J. Meier,et al. When is the graph product of hyperbolic groups hyperbolic? , 1996 .
[147] J. Tits. Structures et groupes de Weyl , 1966 .
[148] V. Jones. Von Neumann Algebras , 2020, Lectures on von Neumann Algebras.
[149] J. Dodziuk. De Rham-Hodge theory for L2-cohomology of infinite coverings , 1977 .
[150] Bruna Tanaka Cremonini,et al. Buildings , 1995, Data, Statistics, and Useful Numbers for Environmental Sustainability.
[151] Daniel T. Wise,et al. Special Cube Complexes , 2008, The Structure of Groups with a Quasiconvex Hierarchy.
[152] M. Kervaire. Smooth homology spheres and their fundamental groups , 1969 .
[153] A. Kuku,et al. Higher Algebraic K-Theory , 2006 .
[154] M. Bridson,et al. Metric Spaces of Non-Positive Curvature , 1999 .
[155] Bernhard Mühlherr,et al. Rigidity of Coxeter Groups and Artin Groups , 2002 .
[156] Michael W. Davis. Nonpositive Curvature and Reflection Groups , 2001 .
[157] P. Caprace. Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls , 2005, math/0508057.
[158] J. Millson. On the first Betti number of a constant negatively curved manifold , 1976 .
[159] C. Wall. Finiteness conditions for CW-complex I , 1965 .
[160] H. Hopf,et al. Enden offener Räume und unendliche diskontinuierliche Gruppen , 1943 .
[161] D. Allcock. Infinitely many hyperbolic Coxeter groups through dimension 19 , 2006, 0903.0138.
[162] J. Dodziuk. L^2-harmonic forms on rotationally symmetric Riemannian manifolds , 1979 .
[163] Some examples of discrete group actions on aspherical manifolds , 2003 .
[164] H. Fischer. Boundaries of right-angled Coxeter groups with manifold nerves , 2003 .
[165] J. Tits,et al. On buildings and their applications , 1975 .
[166] W. Thurston,et al. Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.
[167] R. Bott. An application of the Morse theory to the topology of Lie-groups , 1956 .
[168] Richard M. Weiss,et al. The Structure of Spherical Buildings , 2004 .
[169] Noel Brady,et al. Morse theory and finiteness properties of groups , 1997 .
[170] T. Januszkiewicz,et al. Fundamental Groups of Blow-ups , 2002 .
[171] J. Świa̧tkowski,et al. Hyperbolic Coxeter groups of large dimension , 2003 .
[172] P. McMullen,et al. Combinatorially regular polytopes , 1967 .
[173] Matthew Dyer,et al. Reflection subgroups of Coxeter systems , 1990 .
[174] John R. Harper,et al. Algebraic topology : a first course , 1982 .
[175] Vinay V. Deodhar. On the root system of a coxeter group , 1982 .
[176] Graham A. Niblo,et al. Coxeter Groups act on CAT(0) cube complexes , 2003 .
[177] D. Barnette. A proof of the lower bound conjecture for convex polytopes. , 1973 .
[178] H. Coxeter. REGULAR HONEYCOMBS IN HYPERBOLIC SPACE , 1956 .
[179] Louis Solomon,et al. A decomposition of the group algebra of a finite Coxeter group , 1968 .
[180] Tadeusz Januszkiewicz,et al. Right-angled Artin groups are commensurable with right-angled Coxeter groups , 2000 .
[181] Robert Steinberg,et al. Endomorphisms of linear algebraic groups , 1968 .
[182] Kenneth S. Brown,et al. Cohomology of Groups , 1982 .
[183] Bernhard Mühlherr,et al. On Isomorphisms between Coxeter Groups , 2000, Des. Codes Cryptogr..
[184] John Milnor,et al. Towards the Poincaré Conjecture and the Classification of 3-Manifolds, Volume 50, Number 10 , 2003 .
[185] C. Hodgson,et al. A characterization of compact convex polyhedra in hyperbolic 3-space , 1993 .
[186] Daan Krammer,et al. The conjugacy problem for Coxeter groups , 2009 .
[187] Michael W. Davis. Coxeter groups and aspherical manifolds , 1984 .
[188] Damian Osajda,et al. Boundaries of right-angled hyperbolic buildings , 2006, math/0610114.
[189] W. Jakobsche. Homogeneous cohomology manifolds which are inverse limits , 1991 .
[190] Jacques Tits,et al. Le problème des mots dans les groupes de Coxeter , 1969 .
[191] G. Mess. Examples of Poincaré duality groups , 1990 .
[192] Robion Kirby,et al. Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. , 1977 .
[193] W. Parry. Growth Series of Coxeter Groups and Salem Numbers , 1993 .
[194] Jean-Pierre Serre. Cohomologie des groupes discrets , 1971 .
[195] C D Papakyriakopoulos,et al. ON DEHN'S LEMMA AND THE ASPHERICITY OF KNOTS. , 1957, Proceedings of the National Academy of Sciences of the United States of America.
[196] A. O. Houcine. On hyperbolic groups , 2006 .
[197] W. Lück. L2-Betti numbers of mapping tori and groups , 1994 .
[198] Bruce Kleiner,et al. Notes on Perelman's papers , 2006 .
[199] S. Smale. Generalized Poincare's Conjecture in Dimensions Greater Than Four , 1961 .
[200] D. V. Alekseevskij,et al. Geometry of Spaces of Constant Curvature , 1993 .
[201] Constantin Gonciulea. Virtual epimorphisms of coxeter groups onto free groups , 2000 .
[202] E. M. Andreev. ON CONVEX POLYHEDRA OF FINITE VOLUME IN LOBAČEVSKIĬ SPACE , 1970 .
[203] E. M. Andreev. ON CONVEX POLYHEDRA IN LOBAČEVSKIĬ SPACES , 1970 .
[204] G. Mostow. Strong Rigidity of Locally Symmetric Spaces. , 1973 .
[205] Abe Shenitzer,et al. The Poincaré Conjecture? , 2006, Am. Math. Mon..
[206] R. Howlett. Normalizers of Parabolic Subgroups of Reflection Groups , 1980 .
[207] È. Vinberg,et al. Spaces of constant curvature , 1993 .
[208] Michaela Davis. The homology of a space on which a reflection group acts , 1987 .
[209] M. Newman. A THEOREM ON PERIODIC TRANSFORMATIONS OF SPACES , 1931 .
[210] W. Mio. Homology manifolds , 1996 .
[211] Barry Mazur,et al. A Note on Some Contractible 4-Manifolds , 1961 .
[212] P. Deligne,et al. Les immeubles des groupes de tresses généralisés , 1972 .
[213] P. Ontaneda. The double of a hyperbolic manifold and non-positively curved exotic PL structures , 2002 .
[214] Stratos Prassidis,et al. Rigidity of Coxeter groups , 2000 .
[215] J. Stallings. The Piecewise-Linear Structure of Euclidean Space , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.
[216] H. Freudenthal,et al. Über die Enden topologischer Räume und Gruppen , 1931 .
[217] M. Spivak,et al. Spaces satisfying Poincaré duality , 1967 .
[218] Y. Benoist. A survey on divisible convex sets , 2022 .
[219] S. Yau,et al. Compact manifolds of nonpositive curvature , 1972 .
[220] P. Bahls,et al. Reflection Independence in Even Coxeter Groups , 2005 .
[221] H. Donnelly,et al. On the Differential Form Spectrum of Negatively Curved Riemannian Manifolds , 1984 .
[222] È. Vinberg,et al. Hyperbolic reflection groups , 1985 .
[223] Mathématiques DE L’I.H.É.S,et al. Volume and bounded cohomology , 2003 .