Mathematical Sciences: Topics in Homotopy Theory
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause'}
Davis will work on problems in three general areas of                      homotopy theory.  i) A primary goal is to prove that, in the                    Adams spectral sequence converging to the 2-primary stable                      homotopy groups of spheres, the line above which only the image                 of J survives has slope 1/5, or perhaps even 1/6, rather than                   the 3/10 already established.  The odd primary analogue of this                 result will also be considered.  Projects in unstable homotopy                  theory arising from the same circle of ideas include                            determining the v-one-periodic homotopy groups of the special                   orthogonal groups SO(n), the unstable Adams spectral sequence                   for SO, and a better bound on v-zero-torsion in the unstable                    Adams spectral sequence for spheres.  ii) He hopes to study the                 classification of the stable homotopy types of smash products                   of stunted real projective spaces.  iii) He will study a                        conjecture of Landweber relating the complex bordism of a                       finite group to its rank, by first attempting the abelian case.                      These problems all call upon expertise in computing with                   homotopy groups, but the computing will be mainly human rather                  than electronic, with only modest and occasional machine                        assistance.  Flexible branching guided by seasoned intuition is                 expected to surpass brute force.  Geometric applications are                    envisioned for the results of these calculations, which will                    provide new tools for the use of topologists.
{'FirstName': 'Donald', 'LastName': 'Davis', 'EmailAddress': 'dmd1@lehigh.edu', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Lehigh University', 'CityName': 'Bethlehem', 'ZipCode': '180153005', 'PhoneNumber': '6107583021', 'StreetAddress': 'Alumni Building 27', 'CountryName': 'United States', 'StateName': 'Pennsylvania', 'StateCode': 'PA'}
{'Code': '1267', 'Text': 'TOPOLOGY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1989&All=true', 'xml': '8900272.xml'}