Given a group G of automorphisms of a matroid M, we describe the representations of G on the homology of the independence complex of the dual matroid M∗ . These representations are related to the homology of the lattice of flats of M, and (when M is realizable) to the top cohomology of a hyperplane arrangement. Finally, we analyze in detail the case of the complete graph, which has applications to algebraic geometry.
Representations of automorphism groups on the homology of matroids / Moci Luca; GIan Marco Pezzoli. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 94:(2021), pp. 103312.1-103312.17. [10.1016/j.ejc.2021.103312]
Representations of automorphism groups on the homology of matroids
Moci Luca;GIan Marco Pezzoli
2021
Abstract
Given a group G of automorphisms of a matroid M, we describe the representations of G on the homology of the independence complex of the dual matroid M∗ . These representations are related to the homology of the lattice of flats of M, and (when M is realizable) to the top cohomology of a hyperplane arrangement. Finally, we analyze in detail the case of the complete graph, which has applications to algebraic geometry.| File | Dimensione | Formato | |
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Open Access dal 08/02/2023
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