1. Representations of automorphism groups on the homology of matroids
- Author
-
Gian Marco Pezzoli, Luca Moci, Moci Luca, and GIan Marco Pezzoli
- Subjects
0102 computer and information sciences ,Algebraic geometry ,Homology (mathematics) ,Mathematics::Algebraic Topology ,01 natural sciences ,Matroid ,Group representation ,Combinatorics ,Mathematics::K-Theory and Homology ,FOS: Mathematics ,Mathematics - Combinatorics ,Algebraic Topology (math.AT) ,Discrete Mathematics and Combinatorics ,Mathematics - Algebraic Topology ,Representation Theory (math.RT) ,0101 mathematics ,Mathematics ,010102 general mathematics ,Complete graph ,homology ,graph ,group representation ,Automorphism ,Cohomology ,010201 computation theory & mathematics ,hyperplane arragements ,matroid ,Combinatorics (math.CO) ,Mathematics - Representation Theory ,Dual matroid - 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.
- Published
- 2021