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Module structure of the
homology of right-angled Artin kernels
Enrique Artal Bartolo, José Ignacio Cogolludo-Agustín, Santiago López de Medrano and Daniel Matei |
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Algebraic & Geometric Topology 22 (2022) 2775–2803
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DOI: 10.2140/agt.2022.22.2775
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Abstract |
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We study the module structure of the homology of Artin kernels, ie kernels of nonresonant characters from right-angled Artin groups onto the integer numbers, where the module structure is with respect to the ring for a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. We provide more properties of the torsion part of this module, eg the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex. |
Keywords
Artin groups, homology
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Mathematical Subject Classification
Primary: 20F36, 20F65, 20J05, 57M07, 57M10
Secondary: 05C69
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References |
Publication
Received: 27 October 2020
Revised: 29 March 2021
Accepted: 28 July 2021
Published: 13 December 2022
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Authors |
| Enrique Artal Bartolo | |
| Departamento de Matemáticas, IUMA,
Facultad de Ciencias Universidad de Zaragoza Zaragoza Spain |
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| José Ignacio Cogolludo-Agustín | |
| Departamento de Matemáticas, IUMA,
Facultad de Ciencias Universidad de Zaragoza Zaragoza Spain |
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| Santiago López de Medrano | |
| Instituto de Matemáticas Universidad Nacional Autónoma de México Mexico City Mexico |
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| Daniel Matei | |
| Institute of Mathematics of the
Romanian Academy Bucharest Romania |
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