Compactifications of Symmetric and Locally Symmetric Spaces

* Preface * Introduction Part I: Compactifications of Riemannian Symmetric Spaces * Review of Classical Compactifications of Symmetric Spaces * Uniform Construction of Compactifications of Symmetric Spaces * Properties of Compactifications of Symmetric Spaces Part II: Smooth Compactifications of Semisimple Symmetric Spaces * Smooth Compactifications of Riemannian Symmetric Spaces G / K * Semisimple Symmetric Spaces G / H * The Real Points of Complex Symmetric Spaces Defined Over R * The DeConcini-Procesi Compactification of a Complex Symmetric Space and its Real Points * The Oshima-Sekiguchi Compactification of G / K and Comparison with G/Hw (R) Part III: Compactifications of Locally Symmetric Spaces * Classical Compactifications of Locally Symmetric Spaces * Uniform Construction of Compactifications of Locally Symmetric Spaces * Properties of Compactifications of Locally Symmetric Spaces * Subgroup Compactifications of o \ G * Metric Properties of Compactifications of Locally Symmetric Spaces o \ X * References * Index

[1]  N. Mok.  Metric Rigidity Theorems On Hermitian Locally Symmetric Manifolds , 1989 .

[2]  I. M. Yaglom,et al.  Felix Klein and Sophus Lie : evolution of the idea of symmetry in the nineteenth century , 1988 .

[3]  G. Mostow.  Strong Rigidity of Locally Symmetric Spaces. , 1973 .

[4]  M. Zworski,et al.  Scattering matrices and scattering geodesics of locally symmetric spaces , 2001 .

[5]  Kazuya Kato,et al.  Borel-Serre Spaces and Spaces of SL(2)-Orbits , 2002 .

[6]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[7]  Eckhard Meinrenken,et al.  LIE GROUPS AND LIE ALGEBRAS , 2021, Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34.

[8]  Marvin Tretkoff,et al.  Introduction to the Arithmetic Theory of Automorphic Functions , 1971 .

[9]  A. Borel,et al.  Introduction aux groupes arithmétiques , 1969 .

[10]  H. Whitney.  Elementary Structure of Real Algebraic Varieties , 1957 .

[11]  Tadao Oda.  Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties , 1987 .

[12]  W. L. Baily,et al.  Compactification of Arithmetic Quotients of Bounded Symmetric Domains , 1966 .

[13]  E. Freitag.  Hilbert Modular Forms , 1990 .

[14]  Ralph Duncan James,et al.  Proceedings of the International Congress of Mathematicians , 1975 .

[15]  Werner Ballmann,et al.  Lectures on Spaces of Nonpositive Curvature , 1995 .

[16]  T. Oshima.  A realization of Riemannian symmetric spaces , 1978 .

[17]  John Hawkes,et al.  Advances in probability and related topics , 1976 .

[18]  A. W. Knapp.  Lie groups beyond an introduction , 1988 .

[19]  J. Loday,et al.  Lie Theory and Its Applications in Physics , 2020, Springer Proceedings in Mathematics & Statistics.

[20]  R. Greene,et al.  Several complex variables and complex geometry , 1991 .

[21]  David L. Degeorge.  Length spectrum for compact locally symmetric spaces of strictly negative curvature , 1977 .

[22]  Carl B. Boyer,et al.  A History of Mathematics. , 1993 .

[23]  J. Cerf.  Topologie de certains espaces de plongements , 1961 .

[24]  M. Goresky,et al.  On the geometry of quadrics and their degenerations , 1988 .

[25]  S. Helgason.  Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .

[26]  H. Schlichtkrull.  Hyperfunctions and harmonic analysis on symmetric spaces , 1984 .

[27]  C. B. Allendoerfer,et al.  Hyperbolic manifolds and holomorphic mappings , 1970 .

[28]  Lo Yang,et al.  International Symposium in Memory of Hua Loo Keng , 1991 .

[29]  L. Ji.  The Greatest Common Quotient of Borel-Serre and the Toroidal Compactifications of Locally Symmetric Spaces , 1998 .

[30]  C. Moore.  Compactifications of Symmetric Spaces II: The Cartan Domains , 1964 .

[31]  A. Reid,et al.  The Arithmetic of Hyperbolic 3-Manifolds , 2002 .

[32]  A. Adem,et al.  On the cohomology of SL(2,Z[1/p]) , 1995, math/9503230.

[33]  L. Ji.  Satake and Martin compactifications of symmetric spaces are topological balls , 1997 .

[34]  K. Burns,et al.  On topological tits buildings and their classification , 1987 .

[35]  J. Carlson,et al.  Complex Geometry and Lie Theory , 1992 .

[36]  Nicolas Bourbaki,et al.  Eléments de Mathématique , 1964 .

[37]  Fritz Grunewald,et al.  Groups Acting on Hyperbolic Space , 1998 .

[38]  N. Levenberg,et al.  Function theory in several complex variables , 2001 .

[39]  R. Macpherson,et al.  Geometry of compactifications of locally symmetric spaces , 2002 .

[40]  Igor Nikolaev.  Arithmetic of hyperbolic 3-manifolds , 2002 .

[41]  Eduardo Sontag.  Festschrift in Honor of , 2022 .

[42]  Franki Dillen,et al.  Handbook of differential geometry , 2000 .

[43]  C.J.H. Mann,et al.  Remarkable Mathematicians: From Euler to von Neumann , 2006 .

[44]  J. Rosenberg,et al.  Non-Commutative Harmonic Analysis , 2006 .

[45]  J. Milnor,et al.  Prospects in Mathematics , 1971 .

[46]  S. Zucker.  L2 cohomology of warped products and arithmetic groups , 1982 .

[47]  Calvin C. Moore,et al.  COMPACTIFICATIONS OF SYMMETRIC SPACES. , 1964 .

[48]  A. Borel,et al.  Corners and arithmetic groups , 1973 .

[49]  R. Dijkgraaf,et al.  The moduli space of curves , 1995 .

[50]  Robert S. Martin,et al.  Minimal positive harmonic functions , 1941 .

[51]  小林 昭七.  Hyperbolic manifolds and holomorphic mappings , 1970 .

[52]  T. Oshima.  A Realization of Semisimple Symmetric Spaces and Construction of Boundary Value Maps , 1988 .

[53]  Nellie Clarke Brown.  Trees , 1896, Savage Dreams.

[54]  A. Borel.  Automorphic Forms on Sl2 (R) , 1997 .

[55]  Metric compactifications of locally symmetric spaces , 1998 .

[56]  Andrei S. Rapinchuk,et al.  Algebraic groups and number theory , 1992 .

[57]  C. Wall.  Homological Group Theory , 1980 .

[58]  Jiang-Hua Lu,et al.  On the variety of Lagrangian subalgebras , 1999, math/9909005.

[59]  Valeri V.Dolotin.  On Invariant Theory , 1995, alg-geom/9512011.

[60]  R. Holzapfel.  Geometry and arithmetic around Euler partial differential equations , 1986 .

[61]  G. Geer.  Hilbert Modular Surfaces , 1988 .

[62]  S. Kung,et al.  International symposium in memory of Hua Loo Keng , 1991 .

[63]  R. Hain,et al.  Mapping Class Groups and Moduli Spaces of Riemann Surfaces , 1993 .

[64]  Armand Borel.  Linear Algebraic Groups , 1991 .

[65]  吉田 正章,et al.  Hypergeometric functions, my love : modular interpretations of configuration spaces , 1997 .

[66]  P. Malliavin,et al.  Factorisations et lois limites de la diffusion horizontale au-dessus d'un espace riemannien symetrique , 1974 .

[67]  M. Raghunathan.  Discrete subgroups of Lie groups , 1972 .

[68]  R. Holzapfel.  The Ball and Some Hilbert Problems , 2004 .

[69]  J. Schwermer,et al.  Cohomology of Arithmetic Groups and Automorphic Forms , 1990 .

[70]  Michael E. Taylor,et al.  Differential Geometry I , 1994 .

[71]  S. D. Chatterji.  Proceedings of the International Congress of Mathematicians , 1995 .

[72]  Bruna Tanaka Cremonini,et al.  Buildings , 1995, Data, Statistics, and Useful Numbers for Environmental Sustainability.

[73]  I. Satake.  On Compactifications of the Quotient Spaces for Arithmetically Defined Discontinuous Groups , 1960 .

[74]  L. Ji.  Buildings and their Applications in Geometry and Topology , 2006 .

[75]  Jörg M. Wills,et al.  Handbook of Convex Geometry , 1993 .

[76]  T. Ohsawa,et al.  Prospects in Complex Geometry , 1991 .

[77]  N. Wallach.  Introductory lectures on automorphic forms , 2001 .

[78]  E. W. Morris.  No , 1923, The Hospital and health review.

[79]  A. Borel,et al.  Algebraic groups and discontinuous subgroups , 1966 .

[80]  I. Satake,et al.  ON REPRESENTATIONS AND COMPACTIFICATIONS OF SYMMETRIC RIEMANNIAN SPACES , 1960 .

[81]  志村 五郎,et al.  Introduction to the arithmetic theory of automorphic functions , 1971 .

[82]  V. Molchanov,et al.  Harmonic analysis on homogeneous spaces , 1973 .

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

[84]  C. Siegel,et al.  Lectures on the Geometry of Numbers , 1989 .

[85]  W. Schmid,et al.  Some remarks on L2 and intersection cohomologies , 1987 .

[86]  Harry Furstenberg,et al.  A POISSON FORMULA FOR SEMI-SIMPLE LIE GROUPS* , 1963 .

[87]  Remarks on the wonderful compactification of semisimple algebraic groups , 1999 .

[88]  Gregory Margulis,et al.  Discrete Subgroups of Semisimple Lie Groups , 1991 .

[89]  L. Ehrenpreis,et al.  Theta functions, Bowdoin 1987 , 1989 .

[90]  R. Connelly.  In Handbook of Convex Geometry , 1993 .

[91]  Dmitrij Borisovich Fuks,et al.  Beginner’s Course in Topology , 1984 .

[92]  Harish-Chandra.  Representations of Semisimple Lie Groups VI: Integrable and Square-Integrable Representations , 1956 .

[93]  T. Oshima,et al.  The Restricted Root System of a Semisimple Symmetric Pair , 1984 .

[94]  J. Taylor.  The Martin compactification associated with a second order strictly elliptic partial differential operator on a manifold , 2001 .

[95]  Y. Flicker.  ON AUTOMORPHIC FORMS , 2005 .

[96]  T. Oshima,et al.  Eigenspaces of invariant differential operators on an affine symmetric space , 1980 .

[97]  D. Sullivan.  Related aspects of positivity in Riemannian geometry , 1987 .

[98]  S. Krantz.  Function theory of several complex variables , 1982 .

[99]  H. Schlichtkrull,et al.  Harmonic Analysis on semisimple symmetric spaces. A survey of some general results. , 1997 .

[100]  J. Conway.  Understanding groups like G 0 N , 1996 .

[101]  Elisabetta Stricland.  A vanishing theorem for group compactifications , 1987 .

[102]  S. Yau.  Seminar on differential geometry , 1982 .

[103]  E. Strickland.  Computing the equivariant cohomology of group compactifications , 1991 .

[104]  Phillip A. Griffiths,et al.  Complex analysis and algebraic geometry , 1979 .

[105]  P. Eymard,et al.  Analyse Harmonique sur les Groupes de Lie II , 1975 .

[106]  Ioan Mackenzie James.  Remarkable Mathematicians: From Euler to von Neumann , 2002 .

[107]  M. Picardello.  Harmonic analysis and discrete potential theory , 1992 .

[108]  Lizhen Ji,et al.  Compactifications of Symmetric Spaces , 1998 .

[109]  W. Magnus.  Noneuclidean tesselations and their groups , 1974 .

[110]  B. Blackadar.  Operator Algebras , 1998 .

[111]  Robert P. Janglands.  The Zeta Functions of Picard Modular Surfaces , 1992 .

[112]  W. Schmid,et al.  Variations of polarized hodge structure: Asymptotics and monodromy , 1987 .

[113]  L. Ji,et al.  Heat Kernel and Green Function Estimates on Noncompact Symmetric Spaces , 1999 .