Loop spaces and the compression theorem

Wiest, Bert

doi:10.1090/S0002-9939-00-05472-1

Loop spaces and the compression theorem
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Proc. Amer. Math. Soc. 128 (2000), 3741-3747 Request permission

Abstract:

For a smooth, finite-dimensional manifold $M$ with a submanifold $S$ we study the topology of the straight loop space $\Omega ^{st}_SM$, the space of loops whose intersections with $S$ are subject to a certain transversality condition. Our main tool is Rourke and Sanderson’s compression theorem. We prove that the homotopy type of the straight loop space of a link in $S^3$ depends only on the number of link components.

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