Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds

Abstract: Frøyshov invariants are subtle numerical topological invariants of rational homology three-spheres derived from gradings in monopole Floer homology. In this talk I will look at their relation with invariants arising from hyperbolic geometry (such as volumes and lengths of closed geodesics), using an odd version of the Selberg trace formula and ideas from analytic number theory. In particular, for the class of minimal L-spaces, I will describe an effective procedure to compute them taking as input explicit geometric data, and show for example how this can be used to determine all the Frøyshov invariants for the Seifert-Weber dodecahedral space. This is joint work with M. Lipnowski (McGill).

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The livestream is on Zoom at : uqam.zoom.us/j/98999725241 (no password is needed).

The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA