Homotopical Intersection Theory, III: multi-relative intersection problems
Algebraic Topology
2019-05-29 v4 Geometric Topology
Abstract
This paper extends some results of Hatcher and Quinn 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 it can be deformed off of any proper subcollection in a homotopy coherent way. In a certain range of dimensions, ours is a complete obstruction to finding the desired deformation. We apply this machinery to embedding problems and to the study of linking phenomena.
Cite
@article{arxiv.1212.4420,
title = {Homotopical Intersection Theory, III: multi-relative intersection problems},
author = {John R. Klein and Bruce Williams},
journal= {arXiv preprint arXiv:1212.4420},
year = {2019}
}
Comments
This is the final pre-publication version. The main technical result is now deduced using functor calculus (this simplifies the exposition considerably). The article is to appear in AGT