1. Bounding the gap between a free group (outer) automorphism and its inverse
- Author
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Ladra, M., Silva, P., and Ventura, E.
- Abstract
For any finitely generated group $$G$$ G , two complexity functions $$\alpha _G$$ αG and $$\beta _G$$ βG are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of $$G$$ G and the norm of its inverse. Restricting attention to free groups $$F_r$$ Fr , the exact asymptotic behaviour of $$\alpha _2$$ α2 and $$\beta _2$$ β2 is computed. For rank $$r\geqslant 3$$ r⩾3 , polynomial lower bounds are provided for $$\alpha _r$$ αr and $$\beta _r$$ βr , and the existence of a polynomial upper bound is proved for $$\beta _r$$ βr .
- Published
- 2016
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