Minimal volume entropy of free-by-cyclic groups and 2-dimensional right-angled Artin groups
| Autor: | Matt Clay, Corey Bregman |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Fundamental group Group (mathematics) General Mathematics 010102 general mathematics Geometric Topology (math.GT) Cyclic group Group Theory (math.GR) 01 natural sciences Mathematics - Geometric Topology Entropy (classical thermodynamics) Simplicial complex 0103 physical sciences FOS: Mathematics Artin group Minimal volume 010307 mathematical physics 20F65 57M07 0101 mathematics Algebraic number Mathematics - Group Theory Mathematics |
| Zdroj: | Mathematische Annalen. 381:1253-1281 |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-021-02211-9 |
| Popis: | Let $G$ be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to $G$ has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criterion is shown by analyzing the fiber $\pi_1$-growth collapse and non-collapsing assumptions of Babenko-Sabourau. Comment: 25 pages, 2 figures; v2: corrected error in statement and proof of Theorem 3.3, main results unchanged |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink