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2019 Homotopical intersection theory, III: Multirelative intersection problems
John R Klein, Bruce Williams
Algebr. Geom. Topol. 19(3): 1079-1134 (2019). DOI: 10.2140/agt.2019.19.1079

Abstract

We extend some results of Hatcher and Quinn (1974) beyond the metastable range. We give a bordism-theoretic obstruction χ ( f ) to deforming a map f : P N between manifolds simultaneously off of a collection of pairwise disjoint submanifolds Q 1 , , Q j N under the assumption that f can be deformed off of any proper subcollection in a homotopy coherent way. In a certain range of dimensions, χ ( f ) 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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John R Klein. Bruce Williams. "Homotopical intersection theory, III: Multirelative intersection problems." Algebr. Geom. Topol. 19 (3) 1079 - 1134, 2019. https://doi.org/10.2140/agt.2019.19.1079

Information

Received: 23 November 2016; Revised: 22 August 2018; Accepted: 24 October 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07078601
MathSciNet: MR3954276
Digital Object Identifier: 10.2140/agt.2019.19.1079

Subjects:
Primary: 55N45, 55R70, 57N65
Secondary: 57Q45, 57R40, 57R85, 57R91

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2019
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