تقرير
On the Girth of Groups acting on CAT(0) cube complexes
| العنوان: | On the Girth of Groups acting on CAT(0) cube complexes |
|---|---|
| المؤلفون: | Banerjee, Arka, Gulbrandsen, Daniel, Mishra, Pratyush, Parija, Prayagdeep |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Geometric Topology, 20F65, 20F67 |
| الوصف: | We obtain a sufficient condition for lattices in the automorphism group of a finite dimensional CAT(0) cube complex to have infinite girth. As a corollary, we get a version of Girth Alternative for groups acting geometrically: any such group is either {locally finite}-by-{virtually abelian} or it has infinite girth. We produce counterexamples to show that the alternative fails in the general class of groups acting cocompactly on finite dimensional CAT(0) cube complexes by obtaining examples of non virtually solvable groups which satisfy a law. Comment: 20 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.09091 |
| رقم الأكسشن: | edsarx.2408.09091 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |