Séminaire à 10h45 puis à 13h45 en ligne via BBB : http://bigbluebutton3.imj-prg.fr/b/cla-jeh-jn7
10h45 : Dusan Joksimovic (IMJ-PRG)
Title: Generating sets of symplectic capacities
Abstract: In
this talk, we address a problem by K. Cieliebak, H. Hofer, J. Latschev,
and F. Schlenk (CHLS) that is concerned with finding a minimal
generating
system for (symplectic) capacities on a given symplectic category. In a
joint work with F. Ziltener, we show
that under some mild hypotheses every countably Borel-generating set of
(normalized) capacities has cardinality bigger than the continuum. This
appears
to be the first result regarding the problem of CHLS, except for a
result by
D. McDuff, stating that the ECH-capacities are monotonely generating for
the
category of ellipsoids in dimension 4. We will also discuss relations
between the problem of finding generating sets and the problem of
recognition and representability of symplectic capacities.
13h45 : Sarah Rasmussen (Cambridge)
Title: Taut foliations from left orders in Heegaard genus 2
Abstract: Until now, taut foliations on non-fibered hyperbolic 3-manifolds have
generally been constructed using branched surfaces, whether via
sutured manifold hierarchies, spanning surfaces of knot exteriors, or
Dunfield's one-vertex triangulations with foliar orientations. In this
talk, I introduce a novel taut foliation construction that makes no
recourse to branched surfaces. Instead, it starts with a
transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface,
specified by a real line action from a left-invariant order (when
existent) on the fundamental group of the 3-manifold. Relating taut
foliations to fundamental group real line actions is a decades old
question that interested Thurston, Gabai, and Calegari, and has been
revived in recent years by the L-space conjecture. This construction
works reliably for genus 2 Heegaard diagrams satisfying mild
conditions, explaining certain numerical results of Dunfield.
Abstract: Until now, taut foliations on non-fibered hyperbolic 3-manifolds have
generally been constructed using branched surfaces, whether via
sutured manifold hierarchies, spanning surfaces of knot exteriors, or
Dunfield's one-vertex triangulations with foliar orientations. In this
talk, I introduce a novel taut foliation construction that makes no
recourse to branched surfaces. Instead, it starts with a
transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface,
specified by a real line action from a left-invariant order (when
existent) on the fundamental group of the 3-manifold. Relating taut
foliations to fundamental group real line actions is a decades old
question that interested Thurston, Gabai, and Calegari, and has been
revived in recent years by the L-space conjecture. This construction
works reliably for genus 2 Heegaard diagrams satisfying mild
conditions, explaining certain numerical results of Dunfield.
