Handle homology of manifolds

Abstract

We give an entirely geometric proof, without recourse to cellular homology, of the fact that ${\partial }^2=0$ in the chain complex defined by a handle decomposition of a given manifold. Topological invariance of the resulting `handle homology' is a consequence of Cerf theory.

15 pages, 8 figures; v2 includes a discussion of integral homology in the non-orientable case

References in corpus (1)

• The Morse-Witten complex via dynamical systems