Weighted sheaves and homology of Artin groups
| Autor: | Giovanni Paolini, Mario Salvetti |
|---|---|
| Přispěvatelé: | Paolini, Giovanni, Salvetti, Mario |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
05E45
20F36 52C35 Braid group 20F36 Discrete Morse theory Group Theory (math.GR) 010103 numerical & computational mathematics Homology (mathematics) Morse code 01 natural sciences 52C35 law.invention Combinatorics 05E45 law FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Combinatorics Mathematics - Algebraic Topology Cohomology of groups 0101 mathematics discrete Morse theory Mathematics::Symplectic Geometry Mathematics Discrete Morse Theory 010102 general mathematics Artin groups hyperplane arrangements Combinatorics (math.CO) Geometry and Topology Affine transformation Mathematics - Group Theory Artin groups Cohomology of groups Discrete Morse Theory |
| Zdroj: | Algebr. Geom. Topol. 18, no. 7 (2018), 3943-4000 |
| Popis: | We expand the theory of weighted sheaves over posets, and use it to study the local homology of Artin groups. First, we use such theory to relate the homology of classical braid groups with the homology of certain independence complexes of graphs. Then, in the context of discrete Morse theory on weighted sheaves, we introduce a particular class of acyclic matchings. Explicit formulas for the homology of the corresponding Morse complexes are given, in terms of the ranks of the associated incidence matrices. We use such method to perform explicit computations for the new affine case Cn, as well as for the cases An, Bn and An (which were already done before by different methods). We expand the theory of weighted sheaves over posets, and use it to study the local homology of Artin groups. First, we use such theory to relate the homology of classical braid groups with the homology of certain independence complexes of graphs. Then, in the context of discrete Morse theory on weighted sheaves, we introduce a particular class of acyclic matchings. Explicit formulas for the homology of the corresponding Morse complexes are given, in terms of the ranks of the associated incidence matrices. We use such method to perform explicit computations for the new affine case Czn , as well as for the cases An , Bn and Azn (which were already done before by different methods). |
| Databáze: | OpenAIRE |
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