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A non-Hausdorff quaternion multiplication

By K.A. Hardie, S. Salbany, J.J.C. Vermeulen and P.J. Witbooi

Abstract

AbstractWe denote by (S3)′ the barycentric subdivision of the minimal model S3 of the three-dimensional sphere in the category of finite posets and order-preserving functions, op(X) is the poset obtained by reversing the order relations in a poset X. We describe a finite model of a quaternion multiplication in the form of a morphism op(S3)′×(S3)′→S3 that restricts to weak homotopy equivalences on the axes. For such multiplications a version of Hopf's construction can be defined that yields finite models of non-trivial homotopy classes

Publisher: Elsevier B.V.
Year: 2003
DOI identifier: 10.1016/S0304-3975(02)00703-X
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