相关论文: Contact homology and virtual fundamental cycles

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical…

The constructions of the virtual Euler (or moduli) cycles and their properties are explained and developed systematically in the general abstract settings.

We define a relative version of contact homology for contact manifolds with convex boundary, and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.

We construct an associative ring which is a deformation of the quantum cohomology ring of the projective plane. Just as the quantum cohomology encodes the incidence characteristic numbers of rational plane curves, the contact cohomology…

Let Y be a closed connected contact 3-manifold. In the series of papers "Embedded contact homology and Seiberg-Witten Floer cohomology I-V", Taubes defines an isomorphism between the embedded contact homology (ECH) of Y and its…

We generalize some of the fundamental results of algebraic topology from topological spaces to \v{C}ech's closure spaces, also known as pretopological spaces. Using simplicial sets and cubical sets with connections, we define three distinct…

Pseudocycles are geometric representatives for integral homology classes on smooth manifolds that have proved useful in particular for defining gauge-theoretic invariants. The Borel-Moore homology is often a more natural object to work with…

We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…

We first describe the action of the fundamental group of a closed surface of variable negative curvature on the oriented geodesics in its universal covering in terms of a naturally-defined flat connection whose holonomy lies in the group of…

We determine the homotopy type of isotropic torus complements in closed contact manifolds in terms of Reeb dynamics of special contact forms. For that we utilize holomorphic curve techniques known from symplectic field theory as…

We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

Co-oriented contact manifolds quite generally describe classical dynamical systems. Quantization is achieved by suitably associating a Schr\"odinger equation to every path in the contact manifold. We quantize the standard contact seven…

This paper is the sequel to the previous paper [Ne15], which showed that sufficient regularity exists to define cylindrical contact homology in dimension three for nondegenerate dynamically separated contact forms, a subclass of dynamically…

In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the…

We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical…

We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…

We give a proof of, for the case of contact structures defined by global contact 1-forms, a Theorem stated by Eliashberg that for any overtwisted contact structure on a closed 3-manifold, its contact homology is 0. A different proof is also…

This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits…