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Proceedings of the American Mathematical Society

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On pairs of nonintersecting faces of cell complexes


Author: Philip L. Wadler
Journal: Proc. Amer. Math. Soc. 51 (1975), 438-440
MSC: Primary 57C05
DOI: https://doi.org/10.1090/S0002-9939-1975-0400241-9
MathSciNet review: 0400241
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Abstract: We show that, for all cell complexes whose underlying set is a manifold, $ M$, an alternating sum of numbers of pairs of faces that do not intersect is a topological invariant. This is done by proving that it is a function of the Euler characteristic, $ x$, of $ M$.


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

  • [1] B. Grünbaum, Convex polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967. MR 37 #2085.
  • [2] Wu Wen-tsün, A theory of imbedding, immersion, and isotopy of polytopes in a euclidean space, Science Press, Peking, 1965. MR 0215305

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0400241-9
Keywords: Cell complex, polytope, manifold, incidence number, nonintersecting faces, Euler's relation
Article copyright: © Copyright 1975 American Mathematical Society