Radhika Gupta: Combinatorial isoperimetric inequality for the free factor complex
Thursday, 23.01.2025 11:00 im Raum SR 1D
The study of mapping class group of a surface and the group of outer automorphisms of a free group Out(F) are closely related. The mapping class group acts on various hyperbolic simplicial complexes like the arc complex and the curve complex. Out(F) also acts on some hyperbolic complexes like the free factor complex, free splitting complex and the cyclic splitting complex.
Webb showed that the arc complex of a surface of high enough complexity does not satisfy a combinatorial isoperimetric inequality: that is, for every N, there is a loop of length 4 in the arc complex that only bounds discs containing at least N triangles. He showed that the same is true for the free splitting complex and the cyclic splitting complex associated with Out(F) and concludes that these complexes do not admit a CAT(0) metric with finitely many shapes. On the contrary, he proved that the curve complex satisfies a linear combinatorial isoperimetric inequality. In this talk, we will show that the free factor complex associated with Out(F) also fails to satisfy a combinatorial isoperimetric inequality.
Angelegt am 13.01.2025 von Paulina Weischer
Geändert am 13.01.2025 von Paulina Weischer
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