Robert Macpherson and Arithmetic Groups
نویسندگان
چکیده
We survey contributions of Robert MacPherson to the theory of arithmetic groups. There are two main areas we discuss: (i) explicit reduction theory for Siegel modular threefolds, and (ii) constructions of compactifications of locally symmetric spaces. The former is joint work with Mark McConnell, the latter with Lizhen Ji.
منابع مشابه
Modular Symbols and Hecke Operators
We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and ...
متن کاملThe Geometry and Topology of Quotient Varieties
Let X be a nonsingular projective variety with an algebraic action of a complex torus (c*)n. We study in this thesis the symplectic quotients (reduced phase spaces) and the quotients in a more general sense. As a part of our program, we have developed a general procedure for computing the intersection homology groups of the quotient varieties. In particular, we obtained an explicit inductive fo...
متن کاملSupplements of Bounded Permutation Groups
Let ). < i, be infinite cardinals and let Q be a set of cardinality 'c. The bounded permutation group B. (Q), or simply B2, is the group consisting of all permutations of Q which move fewer than A points in Q. We say that a permutation group G acting on Q is a supplement of B2 if BA G is the full symmetric group on Q. In [7], Macpherson and Neumann claimed to have classified all supplements of ...
متن کاملSupplements of Bounded Groups
Let be innnite cardinals and let be a set of cardinality. The bounded permutation group B ((), or simply B , is the group consisting of all permutations of which move fewer than points in. We say that a permutation group G acting on is a supplement of B if B G is the full symmetric group on. In 7], Macpherson and Neumann claimed to have classiied all supplements of bounded permutation groups. S...
متن کاملThe Topological Trace Formula
The topological trace formula is a computation of the Lefschetz number of a Hecke correspondence C acting on the weighted cohomology groups, defined in [GHM], of a locally symmetric space X . It expresses this Lefschetz number as a sum of contributions from fixed point components of C on the reductive Borel Serre compactification of X . The proof uses the Lefschetz fixed point formula of [GM2]....
متن کامل