Report
Towards a dichotomy for the Reidemeister zeta function
| العنوان: | Towards a dichotomy for the Reidemeister zeta function |
|---|---|
| المؤلفون: | Bondarewicz, Wojciech, Fel'shtyn, Alexander, Zietek, Malwina |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Algebraic Topology, Mathematics - Dynamical Systems, 37C25, 37C30, 22D10, 20E45, 54H20, 55M20 |
| الوصف: | We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$ where $\mathbb Z_p$ the group of p-adic integers. As a consequence, we obtain a dichotomy for the Reidemeister zeta function of a continuous map of a topological space with fundamental group that is non-finitely generated torsion abelian group. We also prove the rationality of the coincidence Reidemeister zeta function for tame endomorphisms pairs of finitely generated torsion-free nilpotent groups, based on a weak commutativity condition. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2202.09776 |
| رقم الانضمام: | edsarx.2202.09776 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |