Calculating the virtual cohomological dimension of the automorphism group of a RAAG
| Autor: | Richard D. Wade, Andrew W. Sale, Matthew B. Day |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Automorphism group
General Mathematics 010102 general mathematics Group Theory (math.GR) Cohomological dimension Automorphism 01 natural sciences Combinatorics Mathematics::Group Theory FOS: Mathematics Rank (graph theory) Artin group 20F65 0101 mathematics Abelian group Mathematics - Group Theory Mathematics |
| DOI: | 10.1112/blms.12418 |
| Popis: | We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in particular it also applies to untwisted automorphism groups and basis-conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe-Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups. Comment: 15 pages, 2 figures. Revised background on RORGs, small changes elsewhere. Accepted to appear in Bulletin of the LMS |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|