A note on homotopy equivalences
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- by R. M. Vogt PDF
- Proc. Amer. Math. Soc. 32 (1972), 627-629 Request permission
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
- 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
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 627-629
- MSC: Primary 55D10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293632-8
- MathSciNet review: 0293632