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Homotopy types of the deleted product of unions of two simplexes


Author: W. T. Whitley
Journal: Proc. Amer. Math. Soc. 33 (1972), 151-155
MSC: Primary 55D15
DOI: https://doi.org/10.1090/S0002-9939-1972-0292078-6
MathSciNet review: 0292078
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Abstract: If X is a space, let $ {X^\ast} = X \times X - D$, where D is the diagonal. If f is a map on X to a space Y, let $ X_f^\ast = \{ (x,y) \in {X^\ast}\vert f(x) \ne f(y)\} $. In this paper we continue our investigation, begun in [6], of the homotopy types of $ {X^\ast}$ and $ X_f^\ast$, and of a question due to Brahana [1, p. 236], as to when the homotopy types of $ {X^\ast}$ and $ X_f^\ast$ are the same. If X is the union of two nondisjoint simplexes, and if f is a simplicial map on X, we are able, using results and techniques developed in [6], to express the homotopy types of $ {X^\ast}$ and $ X_f^\ast$ in terms of spheres, and then to determine when the homotopy types of these spaces are the same.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292078-6
Article copyright: © Copyright 1972 American Mathematical Society

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