Mathematical Sciences: Symmetry Groups in Dynamics and      Topology
{'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 concerns the symmetry groups of shift dynamical               systems, smooth manifolds, and operator algebras.  Ideas from                   algebraic K-theory are applicable to each area and form a common                theme tying together these disparate mathematical constructs.                        Wagoner will study algebraic and homological structure of                  symmetries of sub-shifts of finite type (SFT), sofic, and other                 shift dynamical systems.  Among other problems, three central                   questions for SFT's he will explore are FOG, LIFT, and SHIFT.                   Some of the problems concerning invariants of symmetries of shift               systems have non-commutative versions for C*-algebras.                               The classic Alexander polynomial of a knot in three-                       dimensional space is closely linked to the algebraic K-theory                   group K1.  Recently, other polynomial invariants have been found                for these knots, starting with the work of V. Jones.  Pseudo-                   isotopies and diffeomorphisms of manifolds in a wide range of                   cases (including knot complements) have invariants involving the                algebraic K-theory group K2.  Wagoner will examine whether it is                possible to define new invariants for diffeomorphisms of knots in               analogy with the new knot polynomials.
{'FirstName': 'John', 'LastName': 'Wagoner', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John B Wagoner', 'EmailAddress': 'wagoner@math.berkeley.edu', 'NSF_ID': '000264799', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Berkeley', 'CityName': 'BERKELEY', 'ZipCode': '947101749', 'PhoneNumber': '5106433891', 'StreetAddress': '1608 4TH ST STE 201', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'CA12', 'ORG_UEI_NUM': 'GS3YEVSS12N6', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF CALIFORNIA, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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