DATE:              Friday, December 4, 2009                     

LOCATION:    Hempfield High School, Room 213 (directions at http://www.millersville.edu/~tgts/)  followed by dinner at a place to be determined.

4:30 TALK:  David Hurtubise, Penn State Altoona

                           “Different approaches to the Morse-Bott inequalities”

           Abstract: The classical proof of the Morse-Bott inequalities uses what Bott called the “half-space” method and the Thom isomorphism theorem with local coefficients.  When certain bundles associated to the critical submanifolds are orientable, the classical proof yields the Morse-Bott inequalities without local coefficients. A new proof of the Morse-Bott inequalities without local coefficients was recently found by Banyaga and Hurtubise using the Morse-Smale-Witten complex and an explicit perturbation technique.  Surprisingly, this new proof requires different orientation assumptions than the classical proof of the Morse-Bott inequalities without local coefficients.