Mathematical Sciences: Geometric Questions in Algebraic     Topology
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Professor Mann will investigate two independent projects in             algebraic topology.  These projects study moduli spaces of                      instantons and piecewise linear group actions on piecewise linear               manifolds and bordism modules.                                                          The first project, representing joint work with Professor               C.P. Boyer, continues the ongoing program of Professors Boyer and               Mann to study the geometry of moduli spaces of instantons, which                arise in the differential geometric formulation of Yang-Mills                   gauge theory, by using the theory of iterated loop spaces and                   their associated homology operations.                                                   The second project, representing joint work with Professor              E.Y. Miller, is based in large part on the work of Professors                   Mann and Miller on equivariant function spaces, classifying                     spaces for equivariant piecewise linear structures and associated               action maps.  This work will allow Professor Mann to answer                     geometric questions which, while well-known for smooth manifolds,               are now unknown for piecewise linear manifolds.                                         It is gratifying to find theoretical physics and topology               stimulating each other as in the first project.
{'FirstName': 'Benjamin', 'LastName': 'Mann', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Benjamin M Mann', 'EmailAddress': 'mann@math.unm.edu', 'NSF_ID': '000460129', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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