Geodesic
Homotopical intersection theory, III: Multirelative intersection problems
Klein, John1 ; Williams, Bruce2
1 Department of Mathematics, Wayne State University, Detroit, MI, United States
2 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1079-1134

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 Q1,…,Qj ⊂ 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.

DOI : 10.2140/agt.2019.19.1079
Classification : 55N45, 57N65, 55R70, 57Q45, 57R40, 57R85, 57R91
Keywords: intersection, linking, bordism, Blakers–Massey, functor calculus

Klein, John 1 ; Williams, Bruce 2

1 Department of Mathematics, Wayne State University, Detroit, MI, United States
2 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States 
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Klein, John; Williams, Bruce. Homotopical intersection theory, III: Multirelative intersection problems. Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1079-1134. doi: 10.2140/agt.2019.19.1079

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