PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Morse-Bott inequalities
Seminar:Topology/Geometry Seminar
Speaker:David Hurtubise (Penn State)
Let f be a Morse-Bott function on a compact finite dimensional manifold M. The polynomial Morse inequalities and an explicit perturbation of f defined using Morse functions on the critical submanifolds of f show immediately that MB(f,t)= P(M,t) + (1+t)R(t), where MB(f,t) is the Morse-Bott polynomial of f and P(M,t) is the Poincare polynomial of M. We prove that R(t) is a polynomial with nonnegative integer coefficients by studying the kernels of the Morse-Smale-Witten boundary operators associated to the Morse functions on the critical submanifolds of f. Our method works when M and all the critical submanifolds are oriented or when Z2-coefficients are used.

Room Reservation Information

Room Number:MB106
Date:10 / 11 / 2007
Time:05:00pm - 06:00pm