Related papers: Contact Structures with Distinct Heegaard Floer In…

In this paper, we apply spectral invariants, constructed in [Oh5,8], to the study of Hamiltonian diffeomorphisms of closed symplectic manifolds $(M,\omega)$. Using spectral invariants, we first construct an invariant norm called the {\it…

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…

We compare two different types of mapping class invariants: the Hochschild homology of an $A_\infty$ bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their…

We construct cobordism maps on link Floer homology associated to decorated link cobordisms. The maps are defined on a curved chain homotopy type invariant. We describe the construction, and prove invariance. We also make a comparison with…

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact…

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in $B^{4}$. In this paper, we describe the set of genera of such surfaces in terms of the $h$-function, which is a link invariant from…

In this article we introduce the topological study of codimension-1 foliations which admit contact or symplectic structures on the leaves. A parametric existence h-principle for foliated contact structures is provided for any cooriented…

We consider deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are a priori non-invariant. Computing their cohomologies, we show that they are not actually biholomorphic to…

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant…

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…

We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration $p\colon W\to D\subset\mathbb{C}$ of a $2n$-dimensional Milnor fiber of the $A_{2\kappa-1}$ singularity. We represent a link…

When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal $\delta$-grading. This leads to the broader class of thin links that one would like to characterize without reference to the…

This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established by Merry-Uljarevi\'c. Our quantitative approach applies to arbitrary admissible contact Hamiltonian…

Let $G$ be a group with a finite balanced presentation $P$. We associate a Heegaard Floer homology group $\widehat{HF}_P(G)$ with the pair $(G,P)$ based on some extra choices and technical assumptions. We show that $\widehat{HF}_P(G)$ is…

Using bordered Floer theory, we construct an invariant $\widehat{\mathit{HFO}}(Y^{\text{orb}})$ for $3$-orbifolds $Y^{\text{orb}}$ with singular set a knot that generalizes the hat flavor $\widehat{\mathit{HF}}(Y)$ of Heegaard Floer…

For any Anosov diffeomorphims on a closed odd dimensional manifold, there exists no invariant contact structure.

We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology. The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient…

We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is…

The scope of the paper is threefold. First, we build on recent work by Hayden to compute Hedden's tau-invariant $\tau_{\xi}(L)$ in the case when $\xi$ is a Stein fillable contact structure on a rational homology sphere, and $L$ is a…

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with…