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arXiv · 1709.08734

Spaces which invert weak homotopy equivalences

Jonathan Ariel Barmak
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Abstract

It is well known that if $X$ is a CW-complex, then for every weak homotopy equivalence $f:A\to B$, the map $f_*:[X,A]\to [X,B]$ induced in homotopy classes is a bijection. For which spaces $X$ is $f^*:[B,X]\to [A,X]$ a bijection for every weak equivalence $f$? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.

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Jonathan Ariel Barmak. 2017-09-25. Spaces which invert weak homotopy equivalences. https://doi.org/10.1017/s0013091518000639

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