Geometrisation of 3-Manifolds

[1]  M. Gromov.  Volume and bounded cohomology , 1982 .

[2]  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 .

[3]  W. Thurston.  The geometry and topology of three-manifolds , 1979 .

[4]  Dan Knopf,et al.  An example of neckpinching for Ricci flow on $S^{n+1}$ , 2004 .

[5]  R. Hamilton.  A Compactness Property for Solutions of the Ricci Flow , 1995 .

[6]  F. González-Acuña,et al.  A note on Hempel–McMillan coverings of 3-manifolds , 2007 .

[7]  Wan-Xiong Shi.  Complete noncompact three-manifolds with nonnegative Ricci curvature , 1989 .

[8]  Gerhard Huisken,et al.  Mean curvature flow with surgeries of two–convex hypersurfaces , 2009 .

[9]  B. Eckmann.  Poincaré Duality Groups of Dimension Two are Surface Groups , 1987 .

[10]  J. Otal.  Thurston's Hyperbolization of Haken Manifolds , 1996 .

[11]  Stephen Smale,et al.  DIFFEOMORPHISMS OF THE 2-SPHERE , 1959 .

[12]  G. Perelman.  The entropy formula for the Ricci flow and its geometric applications , 2002, math/0211159.

[13]  Efficient fundamental cycles of cusped hyperbolic manifolds , 2000, math/0007003.

[14]  J. Hillman.  Indecomposable PD3-complexes , 2012 .

[15]  R. Hamilton.  Three-manifolds with positive Ricci curvature , 1982 .

[16]  한성민,et al.  3 , 1823, Dance for Me When I Die.

[17]  J. Morgan,et al.  Ricci Flow and the Poincare Conjecture , 2006, math/0607607.

[18]  G. Perelman.  Finite extinction time for the solutions to the Ricci flow on certain three-manifolds , 2003, math/0307245.

[19]  Sergei Matveev,et al.  Algorithmic Topology and Classification of 3-Manifolds , 2003 .

[20]  Klaus Johannson,et al.  Homotopy Equivalences of 3-Manifolds with Boundaries , 1979 .

[21]  V. Kapovitch.  Perelman???s Stability Theorem , 2007, math/0703002.

[22]  Don Zagier,et al.  Volumes of hyperbolic three-manifolds , 1985 .

[23]  T. Ivey.  Ricci solitons on compact three-manifolds , 1993 .

[24]  M. Boileau,et al.  Geometrization of 3-orbifolds of cyclic type , 1998, math/9805073.

[25]  Joan Porti,et al.  Three-Dimensional Orbifolds and Their Geometric Structures , 2003 .

[26]  R. Greene,et al.  Lipschitz convergence of Riemannian manifolds. , 1988 .

[27]  W. Thurston,et al.  Lower bounds on volumes of hyperbolic Haken 3-manifolds , 1999, math/0506338.

[28]  William Jaco,et al.  Lectures on three-manifold topology , 1980 .

[29]  On the l-Function and the Reduced volume of Perelman II , 2006, math/0609320.

[30]  L. Bessières,et al.  Collapsing irreducible 3-manifolds with nontrivial fundamental group , 2010 .

[31]  Scalar curvature and the existence of geometric structures on 3-manifolds, II , 2002, math/0202030.

[32]  S. Maillot.  Some applications of Ricci flow to 3-manifolds , 2008, 0801.4881.

[33]  J. Cheeger.  FINITENESS THEOREMS FOR RIEMANNIAN MANIFOLDS. , 1970 .

[34]  D. Mcmillan,et al.  Covering three-manifolds with open cells , 1969 .

[35]  D. Mumford.  The topology of normal singularities of an algebraic surface and a criterion for simplicity , 1961 .

[36]  R. Hamilton.  Non-singular solutions of the Ricci flow on three-manifolds , 1999 .

[37]  Peng Lu,et al.  The Ricci Flow: Techniques and Applications , 2007 .

[38]  Hausdorff Convergence of Riemannian Manifolds and Its Applications , 1990 .

[39]  Michael W. Davis.  The cohomology of a Coxeter group with group ring coefficients , 1998 .

[40]  J. Rubinstein,et al.  An Algorithm to Recognize the 3-Sphere , 1995 .

[41]  B. Chow,et al.  Hamilton's Ricci Flow , 2018 .

[42]  A. V. Chernavsky,et al.  Unrecognizability of manifolds , 2006, Ann. Pure Appl. Log..

[43]  Joan Porti,et al.  Geometrization of 3-dimensional orbifolds , 2000 .

[44]  M. J. Dunwoody,et al.  The algebraic torus theorem , 2000 .

[45]  Mikhael Gromov.  Structures métriques pour les variétés riemanniennes , 1981 .

[46]  Robert Myers.  Simple knots in compact, orientable 3-manifolds , 1982 .

[47]  Geoffrey Hemion,et al.  On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds , 1979 .

[48]  J. Otal.  The hyperbolization theorem for fibered 3-manifolds , 2001 .

[49]  F. G. Acuña,et al.  3-Manifolds that are covered by two open bundles , 2004 .

[50]  J. Hillman.  Three-dimensional Pioncaré duality groups which are extensions , 1987 .

[51]  David Letscher,et al.  Algorithms for essential surfaces in 3-manifolds , 2002 .

[52]  António Salgueiro.  Orders and actions of branched coverings of hyperbolic links , 2009 .

[53]  M. Gromov.  Hyperbolic manifolds according to Thurston and Jørgensen , 1981 .

[54]  W. Haken.  Theorie der Normalflächen , 1961 .

[55]  Friedhelm Waldhausen,et al.  Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I , 1967 .

[56]  Peter Scott.  There are no fake Seifert Fibre Spaces with Infinite π 1 , 1983 .

[57]  J. Morgan.  The Poincaré Conjecture , 2006 .

[58]  Mladen Bestvina,et al.  The boundary of negatively curved groups , 1991 .

[59]  Detlef Gromoll,et al.  On the Structure of Complete Manifolds of Nonnegative Curvature , 1972 .

[60]  William Jaco,et al.  Seifert fibered spaces in 3-manifolds , 1979 .

[61]  Iteration on Teichmüller space , 1990 .

[62]  R. Hamilton.  Four-manifolds with positive curvature operator , 1986 .

[63]  Jeff Cheeger,et al.  Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds , 1982 .

[64]  C. Thomas.  Splitting theorems for certainPD3-groups , 1984 .

[65]  David B. A. Epstein,et al.  Word processing in groups , 1992 .

[66]  B. Chow,et al.  The Ricci Flow : An Introduction I , 2013 .

[67]  J. Hyam Rubinstein,et al.  An Algorithm to Recognise Small Seifert Fiber Spaces , 2004 .

[68]  R. Hamilton.  The Harnack estimate for the Ricci flow , 1993 .

[69]  Ulrich Oertel,et al.  An algorithm to decide if a 3-manifold is a Haken manifold , 1984 .

[70]  I. Holopainen.  Riemannian Geometry , 1927, Nature.

[71]  Canonical metrics on 3-manifolds and 4-manifolds , 2005, math/0511034.

[72]  Kenneth S. Brown,et al.  Cohomology of Groups , 1982 .

[73]  Peter Orlik,et al.  On Seifert-manifolds , 1966 .

[74]  John Milnor,et al.  A Unique Decomposition Theorem for 3-Manifolds , 1962 .

[75]  J. Morgan,et al.  Completion of the Proof of the Geometrization Conjecture , 2008, 0809.4040.

[76]  P. Lu,et al.  Uniqueness of standard solutions in the work of Perelman , 2005 .

[77]  G. Besson,et al.  Ricci flow on open 3–manifolds and positive scalar curvature , 2010, 1001.1458.

[78]  Volume collapsed three-manifolds with a lower curvature bound , 2003, math/0304472.

[79]  Robert Dondero.  Princeton University , 2001 .

[80]  M. Micallef,et al.  Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes , 1988 .

[81]  L. Bessières.  Sur le volume minimal des variétés ouvertes , 2000 .

[82]  J. Hyam Rubinstein,et al.  PL equivariant surgery and invariant decompositions of 3-manifolds , 1989 .

[83]  THE GEOMETRIZATION CONJECTURE AFTER , 2007 .

[84]  G. Besson,et al.  Weak collapsing and geometrisation of aspherical 3-manifolds , 2007, 0706.2065.

[85]  Wan-Xiong Shi.  Ricci deformation of the metric on complete noncompact Riemannian manifolds , 1989 .

[86]  J. Morgan,et al.  Recent progress on the Poincaré conjecture and the classification of 3-manifolds , 2004 .

[87]  D. Burago,et al.  A Course in Metric Geometry , 2001 .

[88]  Walter D. Neumann,et al.  Canonical decompositions of 3–manifolds , 1997, math/9712227.

[89]  R. Hamilton.  Four-manifolds with positive isotropic curvature , 1997 .

[90]  J. Cheeger,et al.  COLLAPSING RIEMANNIAN MANIFOLDS WHILE KEEPING THEIR CURVATURE BOUNDED . II , 2008 .

[91]  William Jaco,et al.  Algorithms for the complete decomposition of a closed $3$-manifold , 1995 .

[92]  Uniqueness of the Ricci flow on complete noncompact manifolds , 2005, math/0505447.

[93]  M. Gromov,et al.  Manifolds of Nonpositive Curvature , 1985 .

[94]  A. Markov,et al.  Insolubility of the Problem of Homeomorphy ∗ , 2001 .

[95]  Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman , 2003, math/0308090.

[96]  W. Haken,et al.  Über das Homöomorphieproblem der 3-Mannigfaltigkeiten. I , 1962 .

[97]  Bruce Kleiner,et al.  Notes on Perelman's papers , 2006 .

[98]  Jianguo Cao,et al.  A Simple Proof of Perelman’s Collapsing Theorem for 3-manifolds , 2010, 1003.2215.

[99]  Jean-Philippe Préaux.  Conjugacy problem in groups of oriented geometrizable 3-manifolds , 2005, math/0512484.

[100]  Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature , 2005, math/0504478.

[101]  H. Seifert,et al.  Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluß) , 1931 .

[102]  Nikolai V. Ivanov,et al.  Foundations of the theory of bounded cohomology , 1987 .

[103]  Z. Sela.  The isomorphism problem for hyperbolic groups I , 1995 .

[104]  Bruce Kleiner,et al.  Locally Collapsed 3-Manifolds , 2010, 1005.5106.

[105]  A. Hatcher,et al.  Notes on Basic 3-Manifold Topology , 2001 .

[106]  Jianguo Cao,et al.  Perelman's collapsing theorem for 3-manifolds , 2009, 0908.3229.

[107]  G. Besson.  Preuve de la conjecture de Poincaré en déformant la métrique par la courbure de Ricci , 2005 .

[108]  Brian H. Bowditch,et al.  Planar groups and the Seifert conjecture , 2004 .

[109]  Hellmuth Kneser,et al.  Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten. , 1929 .

[110]  C. Wall.  Poincare duality in dimension 3 , 2004, math/0410043.

[111]  S. Yau.  Structure of Three-Manifolds - Poincare and geometrization conjectures , 2006 .

[112]  The work of Grigory Perelman , 2007 .

[113]  A. Levine,et al.  New estimates of the storage permanence and ocean co-benefits of enhanced rock weathering , 2023, PNAS nexus.

[114]  H. Seifert,et al.  Topologie Dreidimensionaler Gefaserter Räume , 1933 .

[115]  M. Gromov.  Metric Structures for Riemannian and Non-Riemannian Spaces , 1999 .

[116]  T. Colding,et al.  Width and finite extinction time of Ricci flow , 2007, 0707.0108.

[117]  Li Tao.  AN ALGORITHM TO FIND VERTICAL TORI IN SMALL SEIFERT FIBER SPACES , 2002 .

[118]  Teruhiko Soma.  The Gromov invariant of links , 1981 .

[119]  Friedhelm Waldhausen,et al.  On irreducible 3-manifolds which are sufficiently large * , 2010 .

[120]  Takao Yamaguchi.  A CONVERGENCE THEOREM IN THE GEOMETRY OF ALEXANDROV SPACES , 1996 .

[121]  Friedhelm Waldhausen,et al.  The word problem in fundamental groups of sufficiently large irreducible 3-manifolds , 1968 .

[122]  William Kazez,et al.  Polyhedral minimal surfaces, Heegaard splittings, and decision problems for 3-dimensional manifolds , 1996 .

[123]  B. Leeb,et al.  Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds , 2008, 0801.0803.

[124]  Stanley Peters.  Convergence of riemannian manifolds , 1987 .

[125]  G. Perelman.  Ricci flow with surgery on three-manifolds , 2003, math/0303109.

[126]  F. C. Marques.  Deforming three-manifolds with positive scalar curvature , 2009, 0907.2444.

[127]  J. Manning,et al.  Algorithmic detection and description of hyperbolic structures on closed 3{manifolds with solvable word problem , 2002 .

[128]  John Stillwell,et al.  Three-Dimensional Manifolds , 1980 .

[129]  Terence Tao,et al.  PERELMAN'S PROOF OF THE POINCAR´ E CONJECTURE: A NONLINEAR PDE PERSPECTIVE , 2006, math/0610903.

[130]  Sergey Nikitin.  On 3-manifolds , 2005 .