Groups of PL-homeomorphisms admitting non-trivial invariant characters
Group Theory
2016-04-22 v1
Abstract
We show that several classes of groups G of PL-homeomorphisms of the real line admit non-trivial homomorphisms from G to the additive group of reals that are fixed by every automorphism of G. The classes of groups enjoying the stated property include the generalisations of Thompson's group F studied by K. S. Brown, M. Stein, S. Cleary, and Bieri-Strebel but also the class of groups investigated by Bieri-Neumann-Strebel in [BNS87, Theorem 8.1]. It follows that every automorphism of a group in one of these classes has infinitely many associated twisted conjugacy classes.
Keywords
Cite
@article{arxiv.1511.07088,
title = {Groups of PL-homeomorphisms admitting non-trivial invariant characters},
author = {Daciberg L. Gonçalves and Parameswaran Sankaran and Ralph Strebel},
journal= {arXiv preprint arXiv:1511.07088},
year = {2016}
}
Comments
43 pages; no figures