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

2010/03/29 by Brown, Ronald
#18D15 #55Q05 #55Q52 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.5617

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.

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