Volume 18, issue 7 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Weighted sheaves and homology of Artin groups

Giovanni Paolini and Mario Salvetti

Algebraic & Geometric Topology 18 (2018) 3943–4000
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 C̃n, as well as for the cases An, Bn and Ãn (which were already done before by different methods).

Keywords
Artin groups, hyperplane arrangements, discrete Morse theory
Mathematical Subject Classification 2010
Primary: 05E45, 20F36, 52C35
References
Publication
Received: 4 November 2017
Revised: 19 March 2018
Accepted: 26 June 2018
Published: 11 December 2018
Authors
Giovanni Paolini
Scuola Normale Superiore
Pisa
Italy
Mario Salvetti
Department of Mathematics
University of Pisa
Pisa
Italy