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Automorphisms of free and surface groups and their fixed points

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If you have a question about this talk, please contact Maurice Chiodo .

For a compact surface Σ (orientable or not, and with boundary or not) we show that the fixed subgroup, Fix B, of any family B of endomorphisms of π_1(Σ) is compressed in Σ i.e., rank(Fix B) ≤ rank(H) for any H such that Fix B ≤ H ≤ π_1(Σ). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies the condition rank(Fix φ) ≤ rank(G) for every φ in Aut(G). This is joint work with Q. Zhang and J. Wu.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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