Mathematical Sciences: Transformation Groups on Manifolds   and Varieties
{'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 deals with smooth actions of compact Lie groups            on manifolds and algebraic actions of algebraic groups on affine                varieties.  Here are two of the many problems in the algebraic                  setting:  Are conjugacy classes of algebraic actions of a finite                (reductive) group on a non-singular variety V countable?  In the                case V is complex n-space, is this number finite?                                       Among the aims of the project in the smooth setting:  Give              information on the equivariant surgery obstructions for an                      equivariant normal map in the non-free case (in favorable cases)                in terms of fixed point data, and provide conditions which                      guarantee these obstructions vanish (i.e. give vanishing                        theorems).  Group actions are ubiquitous in nature.                             Understanding them is akin to understanding dynamical systems.
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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