Mathematical Sciences: Applications of Stratified Morse     Theory and Intersection Homology
{'Code': '03040200', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause'}
1. Applications of Intersection Homology:                                     A study will be made of the torsion-linking pairing which exists on             the intersection homology peripheral group of a complex analytic                variety, and, in particular, its relationship with the multiplicity             of the characteristic variety will be studied.                                       Piecewise linear differential forms with singularities will be             constructed for which the L2 forms compute the intersection                     homology, on any simplicial complex which can be (P.L) stratified               with even-codimension strata.                                                        Hecke correspondences which induce homomorphisms on                        intersection homology will be studied, and their Lefschetz numbers              will be calculated using geometric techniques.                                       2.  Applications of Stratified Morse Theory:                               N. Spaltenstein's conjecture relating the intersection homology of              nilpotent varieties and the Poincare polynomial of the complement               of certain arrangements of hyperplanes will be investigated using               the geometric techniques of stratified Morse theory.
{'FirstName': 'R. Mark', 'LastName': 'Goresky', 'EmailAddress': 'goresky@ias.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Northeastern University', 'CityName': 'BOSTON', 'ZipCode': '021155005', 'PhoneNumber': '6173733004', 'StreetAddress': '360 HUNTINGTON AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1267', 'Text': 'TOPOLOGY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8802638.xml'}