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

Philip S. Hirschhorn

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arXiv · 1507.01627

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

Philip S. Hirschhorn

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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 $\lim^{1}$ of the tower of homotopy groups of one dimension higher.

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Philip S. Hirschhorn. 2015-07-06. The homotopy groups of the inverse limit of a tower of fibrations. https://arxiv.org/abs/1507.01627

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