Page 591 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 591
LOW-DIMENSIONAL TOPOLOGY (MS-11)
Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds
Francesco Lin, flin@math.columbia.edu
Columbia University, United States
Coauthor: Michael Lipnowski
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 re-
lation 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 discuss how to obtain effective
upper bounds purely in terms of volume and injectivity radius. Furthermore, I will describe
(again for minimal L-spaces) a 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.
Non-loose negative torus knots
Irena Matkovicˇ, irena.matkovic@maths.ox.ac.uk
University of Oxford, United Kingdom
The Legendrian invariant in knot Floer homology, defined by Lisca, Ozsváth, Stipsicz and Sz-
abó, is torsion for knots in overtwisted structures, and it is non-zero only if the knot is strongly
non-loose as a transverse knot. Using a correspondence between the knot invariants and invari-
ants of contact surgeries, I will show that strongly non-loose transverse realizations of negative
torus knots are classified by their invariants and that their U -torsion order equals one.
Complex vs convex Morse functions and geodesic flow
Burak Özbag˘ci, bozbagci@ku.edu.tr
Koç University, Turkey
Suppose that S is a closed and oriented surface equipped with a Riemannian metric. In the
literature, there are four seemingly distinct constructions of open books on the unit (co)-tangent
bundle of S, having complex, symplectic, contact and Riemannian geometric flavors, respec-
tively. We observe that all of these constructions are based on a suitable choice of a Morse
function on S and show that once such a Morse function is fixed, the resulting open books are
equivalent. This is a joint work with Pierre Dehornoy.
589
Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds
Francesco Lin, flin@math.columbia.edu
Columbia University, United States
Coauthor: Michael Lipnowski
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 re-
lation 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 discuss how to obtain effective
upper bounds purely in terms of volume and injectivity radius. Furthermore, I will describe
(again for minimal L-spaces) a 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.
Non-loose negative torus knots
Irena Matkovicˇ, irena.matkovic@maths.ox.ac.uk
University of Oxford, United Kingdom
The Legendrian invariant in knot Floer homology, defined by Lisca, Ozsváth, Stipsicz and Sz-
abó, is torsion for knots in overtwisted structures, and it is non-zero only if the knot is strongly
non-loose as a transverse knot. Using a correspondence between the knot invariants and invari-
ants of contact surgeries, I will show that strongly non-loose transverse realizations of negative
torus knots are classified by their invariants and that their U -torsion order equals one.
Complex vs convex Morse functions and geodesic flow
Burak Özbag˘ci, bozbagci@ku.edu.tr
Koç University, Turkey
Suppose that S is a closed and oriented surface equipped with a Riemannian metric. In the
literature, there are four seemingly distinct constructions of open books on the unit (co)-tangent
bundle of S, having complex, symplectic, contact and Riemannian geometric flavors, respec-
tively. We observe that all of these constructions are based on a suitable choice of a Morse
function on S and show that once such a Morse function is fixed, the resulting open books are
equivalent. This is a joint work with Pierre Dehornoy.
589
