Abstract. For a smooth, finite-dimensional manifold M with a submanifold S we study the topology of the straight loop space Ωst S M, 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 S3 depends only on the number of link components
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