Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds

Borodzik, Maciej; Powell, Mark

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
• Public URL: https://durham-repository.worktribe.com/output/1343802
• Related Public URLs: https://arxiv.org/abs/1310.2287