Mathematical Sciences: Low-dimensional topology and infinitegroups
{'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}
Professor Shalen will continue his work with H. Gillet on               the structure of groups acting on lambda-trees.  They will then                 explore applications to hyperbolic geometry, K-theory and linear                groups.  Shalen will also continue his work with P. Wagreich on                 growth functions of groups and applications to the study of                     volume and diameters of hyperbolic manifolds, as well as his work               with G. Baumslag and J. Morgan in which properties of finitely                  presented groups are derived from studying their varieties of                   linear representations over fields.                                                     Professors Culler and Shalen will continue their work on                Dehn surgery on knots with the ultimate goal of classifying                     surgeries that give manifolds with cyclic fundamental groups and                settling the Property P conjecture.  They will also work on                     extending the Cyclic Surgery Theorem to links, and interpreting                 the new polynomial invariants for knots and links in terms of                   varieties of groups and representations.                                                Professor Culler will continue his work with K. Vogtmann on             the outer automorphism group of a free group.  They will develop                further the analogy between this group and arithmetic groups.                   Culler will also study the dynamics of these outer automorphisms                in analogy with Thurston's work on dynamics of surface                          automorphisms.  In addition, he will work on constructing                       generalized buildings for a class of goups that includes these                  outer antomorphism groups as well as arithmetic groups and                      mapping class groups.                                                                   Exploring these numerous strong connections between low-                dimensional topology and group theory will advance both fields,                 with ultimate impact on mathematical physics and other heavy                    users of the machinery of modern mathematics, particularly on                   users of precise and concise ways of describing the symmetries of               highly connected spaces.
{'FirstName': 'Peter', 'LastName': 'Shalen', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter B Shalen', 'EmailAddress': 'shalen@uic.edu', 'NSF_ID': '000161185', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Illinois at Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606124305', 'PhoneNumber': '3129962862', 'StreetAddress': '809 S MARSHFIELD AVE M/C 551', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'IL07', 'ORG_UEI_NUM': 'W8XEAJDKMXH3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126700', 'Text': 'TOPOLOGY'}
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