Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Orientable maps and polynomial invariants of free-by-cyclic groups
Speaker: Radhika Gupta, Temple University
Date: February 28, 2022
Time: 20:00:00 Hours
Venue: via Zoom
Abstract: Given a graph map from a graph to itself, we can associate two numbers to it: geometric stretch factor and homological stretch factor. I will define a notion of orientability for graph maps and use it to characterise when the two numbers are equal. The notion of orientability can be upgraded for certain automorphisms of free groups as well. A (fully irreducible) automorphism of a free group determines a free-by-cyclic group to which we can associate two polynomial invariants: the McMullen polynomial and the Alexander polynomial. These polynomials determine the stretch factor and homological stretch factor of f. We will see how orientability helps us to relate these two polynomials.
Title of Talk: Orientable maps and polynomial invariants of free-by-cyclic groups
Speaker: Radhika Gupta, Temple University
Date: February 28, 2022
Time: 20:00:00 Hours
Venue: via Zoom
Abstract: Given a graph map from a graph to itself, we can associate two numbers to it: geometric stretch factor and homological stretch factor. I will define a notion of orientability for graph maps and use it to characterise when the two numbers are equal. The notion of orientability can be upgraded for certain automorphisms of free groups as well. A (fully irreducible) automorphism of a free group determines a free-by-cyclic group to which we can associate two polynomial invariants: the McMullen polynomial and the Alexander polynomial. These polynomials determine the stretch factor and homological stretch factor of f. We will see how orientability helps us to relate these two polynomials.
This is joint work with Spencer Dowdall and Samuel Taylor.