Abstract

We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2014-06-19

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd7085

Keywords

Hecke Action, Arithmetic Cohomology, Sharblies, Modular Symbols

Included in

Mathematics Commons

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