Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds

Borodzik, Maciej; Powell, Mark

doi:10.1007/s12220-014-9538-6

Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds

Borodzik, Maciej; Powell, Mark

Authors

Maciej Borodzik

Mark Powell

Abstract

We prove that an embedded cobordism between manifolds with boundary can be split into a sequence of right product and left product cobordisms, if the codimension of the embedding is at least two. This is a topological counterpart of the algebraic splitting theorem for embedded cobordisms of the first author, A. Némethi and A. Ranicki. In the codimension one case, we provide a slightly weaker statement. We also give proofs of rearrangement and cancellation theorems for handles of embedded submanifolds with boundary.

Citation

Borodzik, M., & Powell, M. (2016). Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds. Journal of Geometric Analysis, 26(1), 57-87. https://doi.org/10.1007/s12220-014-9538-6

Journal Article Type	Article
Online Publication Date	Sep 4, 2014
Publication Date	Jan 1, 2016
Deposit Date	Oct 3, 2017
Publicly Available Date	Oct 4, 2017
Journal	Journal of Geometric Analysis
Print ISSN	1050-6926
Electronic ISSN	1559-002X
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	26
Issue	1
Pages	57-87
DOI	https://doi.org/10.1007/s12220-014-9538-6
Related Public URLs	https://arxiv.org/abs/1310.2287