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Geometry MMA Seminar: Orientability and polynomial invariants for fully irreducible free group automorphisms

Mar 3, 2025, 10:30 - 11:30 AM

 

Speaker: Spencer Dowdall, Vanderbilt University

Title:  Orientability and polynomial invariants for fully irreducible free group automorphisms

 

Abstract:  Every automorphism of a free group comes with two natural notions of growth rate: a homological stretch factor, which is the spectral radius of the action on homology, and a geometric stretch factor that measures the exponential word-length growth of elements under iteration of the automorphism. This talk will explore the relationship between these numbers and explain why they are equal if and only if the automorphism respects a certain type of "orientation" on the free group. By connecting this to certain polynomial invariants, namely the Alexander and McMullen polynomials, we are additionally able to study how this property of orientability manifests among distinct splittings of a given free-by-cyclic groups. Joint work with Radhika Gupta and Samuel J. Taylor.

 

Time: Monday, March 3, 2025 – 10:30am-11:30am

Place: Exploratory Hall, Room 4208

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