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.
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Acknowledgments
The first author wants to thank Indiana University for hospitality and the Fulbright Foundation for a research grant that made this visit possible. He is also supported by Polish OPUS Grant No 2012/05/B/ST1/03195. Part of this work was written while the second author was a visitor at the Max Planck Institute for Mathematics in Bonn, which he would like to thank for its hospitality. The second author gratefully acknowledges an AMS-Simons travel grant which aided his travel to Bonn. The authors are also grateful to the referee for valuable comments.
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Communicated by Marco Abate.
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Borodzik, M., Powell, M. Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds. J Geom Anal 26, 57–87 (2016). https://doi.org/10.1007/s12220-014-9538-6
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DOI: https://doi.org/10.1007/s12220-014-9538-6