English

Handle homology of manifolds

Geometric Topology 2026-02-10 v2 Algebraic Topology

Abstract

We give an entirely geometric proof, without recourse to cellular homology, of the fact that 2=0\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.

Keywords

Cite

@article{arxiv.1811.09055,
  title  = {Handle homology of manifolds},
  author = {Sebastian Durst and Hansjörg Geiges and Marc Kegel},
  journal= {arXiv preprint arXiv:1811.09055},
  year   = {2026}
}

Comments

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