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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on homotopy equivalences


Author: R. M. Vogt
Journal: Proc. Amer. Math. Soc. 32 (1972), 627-629
MSC: Primary 55D10
MathSciNet review: 0293632
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Abstract: Given a homotopy equivalence $ f:X \to Y$, a homotopy inverse g of f, and a homotopy $ H:X \times I \to X$ from $ g \circ f$ to $ {1_X}$. We show that there is a homotopy $ K:Y \times I \to Y$ from $ f \circ g$ to $ {1_Y}$ such that $ f \circ H \simeq K \circ (f \times {1_I})\,{\text{rel}}\,X \times \partial I$ and $ H \circ (g \times {1_I}) \simeq g \circ K\,{\text{rel}}\,Y \times \partial I$.


References [Enhancements On Off] (What's this?)

  • [1] R. Lashof, The immersion approach to triangulation and smoothing, Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 131–164. MR 0317332

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DOI: https://doi.org/10.1090/S0002-9939-1972-0293632-8
Article copyright: © Copyright 1972 American Mathematical Society