Morse functions and cohomology of homogeneous spaces

Abstract

This article arose from a series of three lectures given at the Banach Center, Warsaw, during period of 24 March to 13 April, 2003. Morse functions are useful tool in revealing the geometric formation of its domain manifolds $M$. They define the handle decompositions of $M$ from which the additive homologies $H_{\ast}(M)$ may be constructed. In these lectures two further questions were emphasized. (1) How to find a Morse function on a given manifold? (2) From Morse functions can one derive the multiplicative cohomology rather than the additive homology?