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- W2895383313 abstract "In this paper, we derive an asymptotic formula for the number of conjugacy classes of elements in a class of statistically convex-cocompact actions with contracting elements. Denote by $mathcal C(o, n)$ (resp. $mathcal C'(o, n)$) the set of (resp. primitive) conjugacy classes of pointed length at most $n$ for a basepoint $o$. The main result is an asymptotic formula as follows: $$sharp mathcal C(o, n) asymp sharp mathcal C'(o, n) asymp frac{exp(omega(G)n)}{n}.$$ A similar formula holds for conjugacy classes using stable length. As a consequence of the formulae, the conjugacy growth series is transcendental for all non-elementary relatively hyperbolic groups, graphical small cancellation groups with finite components. As by-product of the proof, we establish several useful properties for an exponentially generic set of elements. In particular, it yields a positive answer to a question of J. Maher that an exponentially generic elements in mapping class groups have their Teichm{u}ller axis contained in the principal stratum." @default.
- W2895383313 created "2018-10-12" @default.
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- W2895383313 date "2022-05-02" @default.
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- W2895383313 title "Counting conjugacy classes in groups with contracting elements" @default.
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