This project investigates collections of all matrices of certain specific types, viewing the collections as geometric objects. Specifically, it is concerned with the calculation of the cohomology rings of certain matrix groups over the finite field of two elements, with coefficients in this same finite field, and with the application of these results to the detection of torsion classes in the integral homology of the mapping class groups of surfaces. The mapping class groups of surfaces with a single fixed boundary component support a homology operation, or equivalently a double loop space structure, that is little understood. Maginnis plans to obtain information about this homology operation by detecting classes in the homology of matrix groups. These matrix groups will include the upper triangular matrices, a Sylow 2-subgroup of the general linear group, and symplectic matrices and their Sylow 2-subgroups. He also plans to study similar matrix groups over the integers.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8801986
Program Officer
Ralph M. Krause
Project Start
Project End
Budget Start
1988-06-15
Budget End
1991-05-31
Support Year
Fiscal Year
1988
Total Cost
$33,000
Indirect Cost
Name
University of Michigan Ann Arbor
Department
Type
DUNS #
City
Ann Arbor
State
MI
Country
United States
Zip Code
48109