Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1603.06730

Mini-course: property of rapid decay

Łukasz Garncarek
View original source ↗Read source document ↗Export metadata ↓

Abstract

These are the notes for the mini-course on the property of rapid decay given at the Erwin Schr\"odinger Institute in Vienna between March 14th and 18th, 2016, as a part of the Measured Group Theory program. They include parts which were omitted during the lectures, and omit some parts which were included in the lectures (and now I think that they shouldn't have been). We explore the definitions of property RD and its permanence properties, discuss the centroid property and relative centroid property defined by Mark Sapir, and give proofs that certain classes of groups have RD.

Explore related subjects

math.GR

Keep this discovery

BibTeXRIS

Łukasz Garncarek. 2016-03-22. Mini-course: property of rapid decay. https://arxiv.org/abs/1603.06730

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reversibility and its asymptotic counting in Picard group

We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.

math.GR↗
arXiv2026

Conjugator length in finitely generated groups

We describe all functions $\mathbb{N}\rightarrow \mathbb{N}$ that can be realized, up to the standard equivalence, as conjugator length functions of finitely generated groups. Furthermore, we show that any two increasing functions $f,g\colon \mathbb N\to \mathbb N$ can be simultaneously realized as conjugator length functions of finitely generated, commensurable (in particular, quasi-isometric) groups.

math.GR↗
arXiv2026

The spectrum of conjugator length functions

A recent program tries to find which functions appear as conjugator length functions. In this note, we show that any (computable) increasing function larger than $n$ appears as $\mathrm{Cl}_G$ for some finitely generated (recursively presented) group. On the other hand, we demonstrate that either $\mathrm{Cl}_G$ must be constant or $\mathrm{Cl}_G(n)\succ n$. Combining these, we obtain a complete description of which functions appear as conjugator length functions of finitely generated groups.

math.GR↗