Embedded Morse theory and relative splitting of cobordisms of manifolds

Borodzik, M. and Powell, M. (2016) Embedded Morse theory and relative splitting of cobordisms of manifolds. Journal of Geometric Analysis, 26(1), pp. 57-87. (doi: 10.1007/s12220-014-9538-6)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Borodzik, M., and Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Geometric Analysis
ISSN (Online):1559-002X
Published Online:04 September 2014
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