Homotopical Intersection Theory, III: multi-relative intersection problems

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.

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

References in corpus (5)

• Calculus III: Taylor Series
• Multiple disjunction for spaces of smooth embeddings
• Homotopical Intersection Theory, I
• Derivatives of the identity and generalizations of Milnor's invariants
• A stable range description of the space of link maps