Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Details Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

2012-01-24

arxiv.org/abs/1201.4934v2

Mathematics

Group Theory

6 pages

Scientific paper

Given a group automorphism $\phi:\Gamma\lr \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_\infty$-property.

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