Morse theory for manifolds with boundary

Maciej Borodzik; András Némethi; Andrew Ranicki

doi:10.2140/agt.2016.16.971

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arXiv · 1207.3066

Morse theory for manifolds with boundary

Maciej Borodzik·András Némethi·Andrew Ranicki

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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.

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Maciej Borodzik, András Némethi, Andrew Ranicki. 2012-07-12. Morse theory for manifolds with boundary. https://doi.org/10.2140/agt.2016.16.971

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