Embedded Morse theory and relative splitting of cobordisms of manifolds

2013/10/08 by Maciej Borodzik, Mark Powell, Borodzik, Maciej +1 · 2 citations
Mathematics · #57Q60 #57R40 #57R70 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.2287

openalex publication_date 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. Nemethi 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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• Equivariant concordance of periodic 2-knots in S⁴
• Families of Morse functions for manifolds with boundary

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