Crossed modules and the homotopy 2-type of a free loop space

Abstract

The question was asked by Niranjan Ramachandran: how to describe the fundamental groupoid of LX, the free loop space of a space X? We give an answer by assuming X to be the classifying space of a crossed module over a group, and then describe completely a crossed module over a groupoid determining the homotopy 2-type of LX. The method requires detailed information on the monoidal closed structure on the category of crossed complexes.

5 pages version 2: 9 pages; more references and reorganised with more detail on the classifying space version 3: corrections and additions

References in corpus (1)

• Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups