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Homotopical
intersection theory, III: Multirelative intersection
problems
John R Klein and Bruce Williams |
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Algebraic & Geometric Topology 19 (2019) 1079–1134
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Abstract |
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We extend some results of Hatcher and Quinn (1974) beyond the metastable range. We give a bordism-theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the assumption that can be deformed off of any proper subcollection in a homotopy coherent way. In a certain range of dimensions, is a complete obstruction to finding the desired deformation. We apply this machinery to embedding problems and to the study of linking phenomena. |
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Keywords
intersection, linking, bordism, Blakers–Massey, functor
calculus
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Mathematical Subject Classification 2010
Primary: 55N45, 57N65, 55R70
Secondary: 57Q45, 57R40, 57R85, 57R91
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References |
Publication
Received: 23 November 2016
Revised: 22 August 2018
Accepted: 24 October 2018
Published: 21 May 2019
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Authors |
| John R Klein | |
| Department of Mathematics Wayne State University Detroit, MI United States |
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| Bruce Williams | |
| Department of Mathematics University of Notre Dame Notre Dame, IN United States |
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