Two results relating nilpotent spaces and cofibrations

Lewis, Robert H.

doi:10.1090/S0002-9939-1978-0507347-7

Two results relating nilpotent spaces and cofibrations
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by Robert H. Lewis PDF

Proc. Amer. Math. Soc. 72 (1978), 403-408 Request permission

Abstract:

We first prove a Blakers-Massey Theorem for nilpotent spaces: If (X, A) is an n-connected, $n \geqslant 1$, pair of nilpotent spaces, then under suitable conditions the map ${\pi _ \ast }(X,A) \to {\pi _ \ast }X/A$ is an isomorphism in dimension $n + 1$ and an epimorphism in dimension $n + 2$. Next, we dualize the well-known fact that if the total space of a fibration is nilpotent, so is the fiber. Our dual theorem can be used to construct new examples of finite nilpotent CW complexes.

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