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2018 Weighted sheaves and homology of Artin groups
Giovanni Paolini, Mario Salvetti
Algebr. Geom. Topol. 18(7): 3943-4000 (2018). DOI: 10.2140/agt.2018.18.3943

Abstract

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 C ̃ n , as well as for the cases A n , B n and à n (which were already done before by different methods).

Citation

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Giovanni Paolini. Mario Salvetti. "Weighted sheaves and homology of Artin groups." Algebr. Geom. Topol. 18 (7) 3943 - 4000, 2018. https://doi.org/10.2140/agt.2018.18.3943

Information

Received: 4 November 2017; Revised: 19 March 2018; Accepted: 26 June 2018; Published: 2018
First available in Project Euclid: 18 December 2018

zbMATH: 1403.05168
MathSciNet: MR3892236
Digital Object Identifier: 10.2140/agt.2018.18.3943

Subjects:
Primary: 05E45, 20F36, 52C35

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 7 • 2018
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