Mathematical Sciences: Knot Theory and Algebraic Geometry inthe Large
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{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
In recent years, interesting classes of knotted and linked                 curves in spaces of dimension 3 have arisen in the study of                     large-scale phenomena in algebraic geometry:  these include                     quasipositive links (cut out, in a sphere of arbitrary radius in                complex 2-space, by a polynomial in two complex variables) and                  links-at-infinity (where the sphere is "infinitely large"); these               links should be very special topologically (e.g., highly                        asymmetric), but it is known that such classical invariants as                  the Alexander polynomial cannot detect this.                                         Also recently, new topological invariants of knots and links               have come to light:  these include the enhanced Milnor number                   (defined for "fibered" links, using differential topology) and                  the generalized Jones polynomial (defined for all links, and                    apparently much more combinatorial in nature); both of these                    invariants detect some asymmetries, and the Jones polynomial was                used to give the first proof that a particular knot (the figure-                8) is not quasipositive.                                                             Now there is evidence that the generalized Jones polynomial                and the enhanced Milnor number are related.  Rudolph plans to                   study this relationship more closely--among other reasons, in                   search of the geometry underlying the generalized Jones                         polynomial.  Quasipositive links and links-at-infinity will serve               as test cases.
{'FirstName': 'Lee', 'LastName': 'Rudolph', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Lee Rudolph', 'EmailAddress': 'lrudolph@black.clarku.edu', 'NSF_ID': '000276738', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Clark University', 'CityName': 'WORCESTER', 'ZipCode': '016101400', 'PhoneNumber': '5084213835', 'StreetAddress': '950 MAIN ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'MA02', 'ORG_DUNS_NUM': '957447782', 'ORG_LGL_BUS_NAME': 'TRUSTEES OF CLARK UNIVERSITY', 'ORG_PRNT_DUNS_NUM': '075349506'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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