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Codimension 2 embeddings, algebraic surg...
Borodzik, Maciej...

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Codimension 2 embeddings, algebraic surgery and Seifert forms by Borodzik, Maciej ( Author )
Lemonjar Open Access
N.A
26-07-2023
We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of algebraic Poincar\'e pairs, which is then applied to describe the behaviour on the chain level of Seifert surfaces of embeddings $M^{2n-1} \subset S^{2n+1}$ under isotopy and cobordism. The second main result (update: which is false) is that the $S$-equivalence class of a Seifert form is an isotopy invariant of the embedding, generalizing the Murasugi--Levine result for knots and links. The third main result is a generalized Murasugi--Kawauchi inequality giving an upper bound on the difference of the Levine--Tristram signatures of cobordant embeddings.
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Article
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English
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MYR 0.01
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http://arxiv.org/abs/1211.5964
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