Armand Borel

Nolan R. Wallach

Deals with two types of cohomology spaces pertaining to reductive Lie group G and a discrete cocompact subgroup. Material presented here naturally divides into two parts, one devoted mainly to real Lie groups, the other to locally compact totally disconnected groups, in particular reductive p-adic groups, or products of real Lie groups and totally disconnected groups. Each part in turn contains roughly three main items: general results on the cohomology used, specific results for cohomology and representations of reductive groups, and applications to discrete cocompact subgroups. This second edition reports on developments in the field since 1980. Annotation copyrighted by Book News, Inc., Portland, OR.

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups

Robert Friedman

John W. Morgan

This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.

Almost Commuting Elements in Compact Lie Groups

This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). Some familiarity with algebraic topology and sheaf theory is assumed.

Intersection Cohomology

Lizhen Ji

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 analysis, number theory, algebraic geometry and algebraic topology

Compactifications of Symmetric and Locally Symmetric Spaces

Lectures Given at the University of Chicago, 1954

Topics in the Homology Theory of Fibre Bundles

American Mathematical Society

W. Casselman

Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions

Armand Borel

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