The minimal genus problem for right angled Artin groups

Boyd, R. , Kastenholz, T. and Mutanguha, J. P. (2023) The minimal genus problem for right angled Artin groups. Geometriae Dedicata, 217(5), 93. (doi: 10.1007/s10711-023-00815-w)

Abstract

We investigate the minimal genus problem for the second homology of a right angled Artin group (RAAG). Firstly, we present a lower bound for the minimal genus of a second homology class, equal to half the rank of the corresponding cap product matrix. We show that for complete graphs, trees, and complete bipartite graphs, this bound is an equality, and furthermore in these cases the minimal genus can always be realised by a disjoint union of tori. Additionally, we give a full characterisation of classes that are representable by a single torus. However, the minimal genus of a second homology class of a RAAG is not always realised by a disjoint union of tori as an example we construct in the pentagon shows.

• Item Type: Articles
• Additional Information: Open Access funding enabled and organized by Projekt DEAL.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Boyd, Dr Rachael
• Authors: Boyd, R., Kastenholz, T., and Mutanguha, J. P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Geometriae Dedicata
• Publisher: Springer
• ISSN: 0046-5755
• ISSN (Online): 1572-9168
• Published Online: 16 August 2023
• Copyright Holders: Copyright © The Author(s) 2023
• First Published: First published in Geometriae Dedicata 217(5):93
• Publisher Policy: Reproduced under a Creative Commons license

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