Loop spaces and the compression theorem
Bert Wiest · Proceedings of the American Mathematical Society · 2000
For a smooth, finite-dimensional manifold M M with a submanifold S S we study the topology of the straight loop space Ω S s t M \Omega ^{st}_SM , the space of loops whose intersections with S 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 S^3 depends only on the number of link components.