Embedded Morse theory and relative splitting of cobordisms of manifolds (Q254235)

In their main theorem, the authors 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 proved by \textit{M. Borodzik}, \textit{A. Némethi} and \textit{A. Ranicki} [``Codimension 2 embeddings, algebraic surgery and Seifert forms'', \url{arXiv:1211.5964}]. The method of proof exploits basic elements of Morse theory for manifolds with boundary, which are very nicely reviewed in the paper.