Algebraic & Geometric Topology

Weighted sheaves and homology of Artin groups

Giovanni Paolini and Mario Salvetti

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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).

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3943-4000.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1545102059

Digital Object Identifier
doi:10.2140/agt.2018.18.3943

Mathematical Reviews number (MathSciNet)
MR3892236

Zentralblatt MATH identifier
1403.05168

Subjects
Primary: 05E45: Combinatorial aspects of simplicial complexes 20F36: Braid groups; Artin groups 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]

Keywords
Artin groups hyperplane arrangements discrete Morse theory

Citation

Paolini, Giovanni; Salvetti, Mario. Weighted sheaves and homology of Artin groups. Algebr. Geom. Topol. 18 (2018), no. 7, 3943--4000. doi:10.2140/agt.2018.18.3943. https://projecteuclid.org/euclid.agt/1545102059


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