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

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

2010-03-29

arxiv.org/abs/1003.5617v3

Mathematics

Algebraic Topology

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

Scientific paper

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.

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