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Two-dimensional weak pseudomanifolds on eight vertices

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Abstract

We explicitly determine all the two-dimensional weak pseudomanifolds on 8 vertices. We prove that there are (up to isomorphism) exactly 95 such weak pseudomanifolds, 44 of which are combinatorial 2-manifolds. These 95 weak pseudomanifolds triangulate 16 topological spaces. As a consequence, we prove that there are exactly three 8-vertex two-dimensional orientable pseudomanifolds which allow degree three maps to the 4-vertex 2-sphere.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Basudeb Datta & Nandini Nilakantan

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  1. Basudeb Datta
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  2. Nandini Nilakantan
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Correspondence to Basudeb Datta.

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Datta, B., Nilakantan, N. Two-dimensional weak pseudomanifolds on eight vertices. Proc. Indian Acad. Sci. (Math. Sci.) 112, 257–281 (2002). https://doi.org/10.1007/BF02829752

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  • DOI: https://doi.org/10.1007/BF02829752

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