Mathematical Sciences: Cohomologies of Matrix Groups amd    Mapping Class Groups
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
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.
{'FirstName': 'John', 'LastName': 'Maginnis', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John Maginnis', 'EmailAddress': None, 'NSF_ID': '000225388', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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