Morse theory for manifolds with boundary
Geometric Topology
2016-05-04 v4 Algebraic Topology
Abstract
We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a topological assumption, a critical point in the interior of a Morse function can be moved to the boundary, where it splits into a pair of boundary critical points. As an application, we prove that every cobordism of manifolds with boundary splits as a union of left product cobordisms and right product cobordisms.
Cite
@article{arxiv.1207.3066,
title = {Morse theory for manifolds with boundary},
author = {Maciej Borodzik and András Némethi and Andrew Ranicki},
journal= {arXiv preprint arXiv:1207.3066},
year = {2016}
}
Comments
v4. 38 pages, 20 figures, minor revision, updated references to Braess, Jankowski--Rubinstein and Hajduk