Canonical forms for free group automorphisms

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Jean Pierre Mutanguha, IAS

Online Talk听

Zoom link:听

The Nielsen-Thurston theory of surface homeomorphism gives: 1) a canonical decomposition of the surface into invariant subsurfaces; and 2) the restriction of our homeomorphisms to these subsurfaces are completely characterized. This can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar decomposition for free group automorphisms. By the defining property of free groups, their automorphisms can have arbitrarily complicated behaviour. This forms a significant barrier to translating specific arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!