Non-contractible configuration spaces

Abstract

Let $F(M,k)$ be the configuration space of ordered $k-$tuples of distinct points in the manifold $M$. Using the Fadell-Neuwirth fibration, we prove that the configuration spaces $F(M,k)$ are never contractible, for $k\ge 2$. As applications of our results, we will calculate the LS category and topological complexity for its loop space and suspension.

arXiv comment9 pages, 1 figure. Readability was improved as requested by the referee. Final version. To appear in Morfismos

References in corpus (1)

• Lusternik-Schnirelmann category of the configuration space of complex projective space

Cited by in corpus (1)

• Equivariant category and Topological complexity of wedges