The topological trace formula
Mark Goresky, Robert MacPherson
TL;DR
This paper derives a Lefschetz trace formula for Hecke correspondences acting on weighted cohomology of locally symmetric spaces and proves their weak hyperbolicity on the reductive Borel-Serre compactification.
Contribution
It introduces a Lefschetz trace formula for Hecke correspondences and establishes their weak hyperbolicity in a new geometric setting.
Findings
Lefschetz formula for Hecke correspondences on weighted cohomology
Proof of weak hyperbolicity of Hecke correspondences on the Borel-Serre compactification
New connections between trace formulas and hyperbolic dynamics
Abstract
The Lefschetz formula for the action of a Hecke correspondence on the weighted cohomology of a locally symmetric space is derived. It is also proven that each Hecke correspondence on the reductive Borel-Serre compactification of the locally symmetric space is weakly hyperbolic.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Mathematical Analysis and Transform Methods