An H-Principle With Boundary Condition

Details An H-Principle With Boundary Condition An H-Principle With Boundary Condition

2010-12-21

arxiv.org/abs/1012.4635v1

Mathematics

Algebraic Topology

33 pages

Scientific paper

We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper to a certain sheaf we find another proof of the homotopy equivalence between the classifying space of a cobordism category and a loop space of the Thom space of the complement of the tautological bundle over the Grassmannians.

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