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arXiv · 1511.07088

Groups of PL-homeomorphisms admitting non-trivial invariant characters

Daciberg L. Gonçalves·Parameswaran Sankaran·Ralph Strebel
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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.

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Daciberg L. Gonçalves, Parameswaran Sankaran, Ralph Strebel. 2015-11-23. Groups of PL-homeomorphisms admitting non-trivial invariant characters. https://arxiv.org/abs/1511.07088

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