The homotopy groups of the inverse limit of a tower of fibrations

2015/07/06 by Hirschhorn, Philip S.
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.01627

Abstract

We carefully present an elementary proof of the well known theorem that each homotopy group (or, in degree zero, pointed set) of the inverse limit of a tower of fibrations maps naturally onto the inverse limit of the homotopy groups (or, in degree zero, pointed sets) of the spaces in the tower, with kernel naturally isomorphic to lim¹ of the tower of homotopy groups of one dimension higher.

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