Lieu: IHP, salle 201
The seminar will take place in presence, but will be broadcasted via zoom
https://us02web.zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 Jonathan Bowden (Regensburg)
Open books, Bourgeois contact structures and their properties.
Abstract:
Twenty years ago Frederic Bourgeois introduced a construction of
contact structures on the product of any contact manifold M with a
2-torus given a choice of compatible open book, whose existence was
proven by Giroux-Mohsen. In particular, this yielded contact structures
on all odd-dimensional tori answering a question of Lutz from the 70’s. A
systematic study of these contact manifolds was initiated by
Lisi-Marinkovic-Niederkrüger and Gironella, the former asking several
questions, which we address in this talk.
In
particular, we show that if the initial contact manifold is
3-dimensional the resulting contact structure is tight, independent of
the initial contact structure and choice of open book. Furthermore,
we show that given ANY contact manifold one can always stabilise the
open book so that the resulting contact structure is not strongly
symplectically fillable. This then yields (many) examples of weakly but
not strongly fillable contact structures in all dimensions. (joint work with F. Gironella and A. Moreno).
12:00 Henri Poincaré (Nancy)
From Floer theory to analysis situs.
Abstract: I'll review some old but revolutionary ideas. I'll use beamer!
14:00 Abror Pirnapasov (Bochum)
Reeb orbits that force topological entropy
Abstract: A transverse link in a contact 3-manifold forces topological
entropy if every Reeb flow possessing this link as a set of periodic
orbits has positive topological entropy. We will explain how cylindrical
contact homology on the complement of transverse links can be used to
show that certain transverse links force topological entropy. As an
application, we show that on every closed contact 3-manifold exists
transverse knots that force topological entropy. We also generalize to
the category of Reeb flows a beautiful result due to Denvir and Mackay,
which says that if a Riemannian metric on the two-dimensional torus has
a contractible closed geodesic, then its geodesic flow has positive
topological entropy. All this is joint work with Marcelo R.R. Alves,
Umberto L. Hryniewicz, and Pedro A.S. Salomão.
BA.
15:45 Guillem Cazassus (Oxford)
Hopf algebras, equivariant Lagrangian Floer homology, and
cornered instanton theory.
Abstract: Let G be a compact Lie group acting on a symplectic manifold M in a Hamiltonian way. If L, L’ is a pair of Lagrangians in M, we show that the Floer complex CF(L,L’) is an A-infinity module over the Morse complex CM(G) (which has an A-infinity algebra structure involving the group multiplication). This permits to define several versions of equivariant Floer homology. This should also imply that the Fukaya categoy Fuk(M), in addition to its own A-infinity structure, is an A-infinity module over CM(G). These two structures should be packaged into a single one: CM(G) is an A-infinity bialgebra, and Fuk(M) is a module over it. In fact, CM(G) should have more structure, it should be a Hopf-infinity algebra, a strong-homotopy structure (still unclear to us) that should induce the Hopf algebra structure on H_*(G). In a certain sense, this refines a conjecture by Teleman.
Applied to some subsets of Huebschmann-Jeffrey’s extended moduli spaces introduced by Manolescu and Woodward, this construction should permit to define a cornered instanton theory analogous to Douglas-Lipshitz-Manolescu’s construction in Heegaard-Floer theory. This is work in progress, joint with Paul Kirk, Mike Miller-Eismeier and Wai-Kit Yeung.
Prochaines séances: 13 mai (I. Di Deda, N. Porcelli, ?), 10 juin (?, ?, ?)
Autre activité symplectique à Paris:
- Symplectic Zoominar (les vendredis hors symplectix à 15:15, heure de Paris)
