10 edition of Compactifications of Symmetric and Locally Symmetric Spaces (Mathematics: Theory & Applications) found in the catalog.
December 8, 2005
by Birkhäuser Boston
Written in English
|The Physical Object|
|Number of Pages||479|
Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to. Smooth Compactifications of Locally Symmetric Varieties, by Avner Ash, David Mumford, Michael Rapoport, Yung-sheng Tai. The book brings together ideas from algebraic geometry, differential geometry, representation theory and number theory, and will continue to prove of value for researchers and graduate students in these areas.
Let X be a Riemannian symmetric space of noncompact type. Let V be a locally symmetric quotient of X by an (arithmetic) lattice such that V has finite volume but is not compact. We investigate geodesic rays in the ends (or cusps) of cally our approach is based on a differential geometric interpretation of well-known facts from the (algebraic) reduction theory of arithmetic groups. This expository article is an expanded version of talks given at the "Current Developments in Mathematics, " conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection cohomology of a real equal-rank Satake compactification of a locally symmetric space with that of the reductive Borel-Serre compactification.
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of appropriate ball quotients. In this paper, we show that their respective toroidal compactifications are isomorphic to moduli spaces of stable pairs as defined in the context of the MMP. CentAUR: Central Archive at the University of Reading. Accessibility navigation. Convergence of measures on compactifications of locally symmetric spaces.
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The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces. Noncompact symmetric and locally symmetric spaces appear in many mathematical theories, including analysis, number theory, algebraic geometry and algebraic topology.
It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate by: Compactifications of the more general semisimple symmetric spaces are also considered.
The book is divided into three main parts. Part I is devoted to five types of compactifications, some related even isomorphic, all G- spaces, of the quotient X=3DG/K of a semisimple linear real Lie group G with finitely many connected components by a maximal.
A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces.
Geometry of compactifications of locally symmetric spaces [ Géométrie des compactifications des espaces localement symétriques ] Ji, Lizhen; Macpherson, Robert. Annales de l'Institut Fourier, Tome 52 () no. 2, pp. Résumé. Locally symmetric spaces. - Now we restrict attention to a manifold M which is a locally symmetric space.
In other words, M = rBX where X is a Riemannian symmetric space with automorphism group G, and f C G is an arithmetic subgroup of G that acts properly and discontinuously on X. In this case, the geodesic compactification exists because.
Symmetric and locally symmetric spaces in general can be regarded as affine symmetric spaces. If M = G / H is a symmetric space, then Nomizu showed that there is a G -invariant torsion-free affine connection (i.e.
an affine connection whose torsion tensor vanishes) on M whose curvature is parallel. * 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/H w (R) Part III: Compactifications of Locally Symmetric Spaces * Classical Compactifications of Locally Symmetric.
History of compactifications 2 New points of view in this book 14 Organization and outline of the book 16 Topics related to the book but not covered and classification of references 17 --Part I Compactifications of Riemannian Symmetric Spaces Review of Classical Compactifications of Symmetric Spaces 27 --I.1 Real.
Abstract. We introduce hyperbolic and asymptotic compactifications of metric spaces and apply them to locally symmetric spaces \GammanX. We show that the reductive Borel--Serre compactification \GammanX RBS is hyperbolic and, as a corollary, get a result of Borel, and Kobayashi--Ochiai that the Baily--Borel compactification \GammanX BB is hyperbolic.
Hermitian symmetric spaces of compact type Definition. Let H be a connected compact semisimple Lie group, σ an automorphism of H of order 2 and H σ the fixed point subgroup of σ. Let K be a closed subgroup of H lying between H σ and its identity compact homogeneous space H / K is called a symmetric space of compact Lie algebra admits a decomposition.
Note that this is just a special case of a general principle to construct compactifications for locally symmetric spaces arising from Anosov representations described in [GKW15] and [KL By "Hermitian locally symmetric space" we mean an arithmetic quotient of a bounded symmetric domain.
Both the toroidal and the reductive Borel-Serre compactifications of such a space. Smooth Compactifications of Locally Symmetric Varieties by Avner Ash,available at Book Depository with free delivery worldwide.
The first two are related to the Borel-Serre compactification and the reductive Borel-Serre compactification of the locally symmetric space Γ\G/K; in fact, they give rise to alternative constructions of these known compactifications.
Ji, Lizhen. Compactifications of Locally Symmetric Spaces. Differential Geom. 73 (), no. 2, MR Borel, Armand; Ji, Lizhen, Compactifications of symmetric and locally symmetric spaces. Mathematics: Theory & Applications. Birkhauser Boston, Boston, MA xvi+ pp.
ISBN: ; 22F30 (11Fxx 22E40 53Cxx). Title: Smooth Compactifications of Locally Symmetric Varieties Format: Paperback Product dimensions: pages, X X in Shipping dimensions: pages, X X in Published: Janu Publisher: Cambridge University Press Language: English.COMPACTIFICATIONS OF LOCALLY SYMMETRIC SPACES denote the resulting set of simple positive roots.
The elements 2 ∆are trivial on SG and form a basis for the character module (S = SG) Z Q. The rational parabolic subgroups which contain Q0 are in one-to-one corre- spondence with subsets I.
The results in this paper are based on a previously constructed exhaustion of a locally symmetric space V=Γ⧹X by Riemannian polyhedra, i.e., compact submanifolds with corners: V=⋃ s⩾0 V(s).We show that the interior of every polyhedron V(s) is homeomorphic to universal covering space X(s) of V(s) is quasi-isometric to the discrete group Γ.