In this paper 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).

Giovanni Paolini, Mario Salvetti (2018). Weighted sheaves and homology of Artin groups. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 18(7), 3943-4000 [10.2140/agt.2018.18.3943].

Weighted sheaves and homology of Artin groups

Giovanni Paolini
;
2018

Abstract

In this paper 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).
2018
Giovanni Paolini, Mario Salvetti (2018). Weighted sheaves and homology of Artin groups. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 18(7), 3943-4000 [10.2140/agt.2018.18.3943].
Giovanni Paolini; Mario Salvetti
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/943215
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