The equivariant Fried conjecture for suspension flow

Abstract: Ray-Singer analytic torsion is a topological invariant of compact manifolds, which can be used to distinguish between homotopy equivalent manifolds that are not homeomorphic. The Ruelle dynamical zeta function is a property of flows on compact manifolds, which encodes information on periodic flow curves. Interestingly, the absolute value of this function at zero is often equal to the analytic torsion of the manifold, even though the latter does not involve the flow at all. Fried’s conjecture is the problem to determine when this equality holds. With Saratchandran, we constructed equivariant versions of analytic torsion and the Ruelle zeta function for proper group actions, and posed the question when an equivariant version of Fried’s conjecture holds. With Pirie, we are investigating this conjecture for a specific type of flows: suspension flows of diffeomorphisms.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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