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/
BYU ScholarsArchive Citation
Cocke, William Leonard, "Hecke Eigenvalues and Arithmetic Cohomology" (2014). Theses and Dissertations. 4130.
https://scholarsarchive.byu.edu/etd/4130
Date Submitted
2014-06-19
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd7085
Keywords
Hecke Action, Arithmetic Cohomology, Sharblies, Modular Symbols
Language
English