Modular symbols and Hecke operators

2000/01/04 by Paul E. Gunnells, Gunnells, Paul E.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.NT #msc:11F67 #msc:11F75

paper · pdf · doi:10.48550/arxiv.math/0001021

11 pp, 2 figures, uses psfrag.sty

arxiv created 2000/01/04 · arxiv updated 2009/11/30

Abstract

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 Some results are unpublished work of Mark McConnell and Robert MacPherson.

Related

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• Computing Hecke Operators for Arithmetic Subgroups of General Linear Groups
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• Introductory computations in the cohomology of arithmetic groups