Related papers: Rabinowitz Floer homology for prequantization bund…

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…

A prequantization bundle is a negative circle bundle over a symplectic surface together with a contact form induced by a S1-invariant connection. Given a symplectically aspherical symplectic filling of a prequantization bundle satisfying…

We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with infinite dimensional symplectic homology: there exists a smoothly embedded ball in such a sphere that cannot be made arbitrarily…

Let M be a closed, connected, orientable 3-manifold. The purpose of this paper is to study the Seiberg-Witten Floer homology of M given that S^1 X M admits a symplectic form. In particular, we prove that M fibers over the circle if M has…

Rabinowitz Floer homology has been investigated on a submanifold of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study…

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on…

In this paper we establish the existence of periodic orbits belonging to any $\sigma$-atoroidal free homotopy class for Hamiltonian systems in the twisted disc bundle, provided that the compactly supported time-dependent Hamiltonian…

Rabinowitz-Floer homology is the Morse-Bott homology in the sense of Floer associated with the Rabinowitz action functional introduced by Kai Cieliebak and Urs Frauenfelder in 2009. In our work, we consider a generalisation of this theory…

We revisit Vafa-Witten theory in the more general setting whereby the underlying moduli space is not that of instantons, but of the full Vafa-Witten equations. We physically derive (i) a novel Vafa-Witten four-manifold invariant associated…

In this paper, Floer homology for Lagrangian submanifolds in an open symplectic manifold given as the complement of a smooth divisor is discussed. The main new feature of this construction is that we do not make any assumption on positivity…

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673].…

We provide a construction of equivariant Lagrangian Floer homology $HF_G(L_0, L_1)$, for a compact Lie group $G$ acting on a symplectic manifold $M$ in a Hamiltonian fashion, and a pair of $G$-Lagrangian submanifolds $L_0, L_1 \subset M$.…

In this article we prove existence of Reeb orbits for Bohr-Sommerfeld Legendrians in certain pre-quantization spaces. We give a quantitative estimate from below. These estimates are obtained by studying Floer homology for fibre-wise…

Given a torus bundle $Y$ over the circle and a cohomology class $[\omega]\in H^2(Y;\mathbb{Z})$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov…

We give an explicit description of the Floer cohomology of a family of Dehn twists about disjoint Lagrangian spheres in a w+ - monotone rational symplectic manifold. As a byproduct of our framework, in a monotone symplectic manifold we are…

We use Floer theory to describe invariants of symplectic $\mathbb{C}^*$-manifolds admitting several commuting $\mathbb{C}^*$-actions. The $\mathbb{C}^*$-actions induce filtrations by ideals on quantum cohomology, as well as filtrations on…

In principle, Floer theory can be extended to define homotopy invariants of families of equivalent objects (e.g. Hamiltonian isotopic symplectomorphisms, 3-manifolds, Legendrian knots, etc.) parametrized by a smooth manifold B. The…

We introduce the notion of symplectic flatness for connections and fiber bundles over symplectic manifolds. Given an $A_\infty$-algebra, we present a flatness condition that enables the twisting of the differential complex associated with…

For a closed symplectic manifold $(M,\omega)$, a compatible almost complex structure $J$, a 1-periodic time dependent symplectic vector field $Z$ and a homotopy class of closed curves $\gamma$ we define a Floer complex based on 1-periodic…

A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and…