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Lusternik–Schnirelmann category of relation matrices on finite spaces and simplicial complexes

Volume 249 / 2020

Kohei Tanaka Fundamenta Mathematicae 249 (2020), 149-167 MSC: Primary 55M30; Secondary 06A07, 05E45. DOI: 10.4064/fm674-8-2019 Published online: 12 December 2019


This paper focuses on matrices associated with maps on finite spaces (posets) and simplicial complexes. A map between finite spaces (simplicial complexes) and its homotopy (contiguous) class can be classified by the associated matrix. As an application, we propose a combinatorial method for calculating the Lusternik–Schnirelmann category of a map on finite spaces. Categorical (contractible) subspaces can be distinguished by a fundamental operation on components of the associated matrix.


  • Kohei TanakaInstitute of Social Sciences
    School of Humanities and Social Sciences
    Academic Assembly
    Shinshu University
    3-1-1 Asahi, Matsumoto
    Nagano 390-8621, Japan

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