Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Prof. Amiya Mukherjee |
Affiliation | : | Indian Statistical Institute, Kolkata |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
January 31, 2007 (Wednesday) |
Title |
: |
Foliations and rational Pontrjagin class |
Abstract | : |
A result of S.P. Novikov applies to prove that
if a map is homotopic to a homeomorphism, then it preserves rational Pontrjagin classes. Also there are examples of homotopy equivalences which do not preserve such classes. In this lecture we outline a proof that a leafwise homotopy equivalence of compact foliated manifolds does preserve rational Pontrjagin classes, if the foliation of its domain has negatively curved leaves. The proof uses the ideas of G. Lusztig, G.G. Kasparov, and A.S. Miscenko, and is a suitable adaptation of their methods to the context of foliations. |