相关论文: Contact homology of Brieskorn manifolds

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

We show that the vanishing of the higher dimensional homology groups of a manifold ensures that every almost CR structure of codimension $k$ may be homotoped to a CR structure. This result is proved by adapting a method due to Haefliger…

Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition…

We construct membrane homology groups $\h(M)$ associated with each compact connected oriented smooth manifold, and show that $\h(M)$ is matrix graded algebra.

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e.,…

Almost contact manifolds with B-metric are considered. There are studied three natural connections (i.e. linear connections preserving the structure tensors) determined by conditions for their torsions. These connections are investigated on…

The $B$-connection on almost complex manifolds with Norden metric is an analogue of the first canonical connection of Lihnerovich in Hermitian geometry. In the present paper it is considered a $B$-connection in the class of the…

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

It is known by the author that there exist 20 families of Dehn surgeries in the Poincar\'e homology sphere yielding lens spaces. In this paper, we give the concrete knot diagrams of the families and extend them to families of lens space…

We formulate the non-commutative integrability of contact systems on a contact manifold $(M,\mathcal H)$ using the Jacobi structure on the space of sections $\Gamma(L)$ of a contact line bundle $L$. In the cooriented case, if the line…

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a…

In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure…

Given a canonically oriented Brieskorn sphere $Y=\Sigma(a_1,...,a_n)$, we confirm some statements conjectured by Gompf. More specifically, we obstruct the existence of rational homology ball symplectic fillings for any contact structure on…

There is one generalization of fibered links in 3-manifolds, called homologically fibered links. It is known that the existence of homologically fibered links whose fiber surface has a given homeomorphic type is determined by the first…

In this article, we classify 1-connected 8-dimensional Poincar\'e complexes, topological manifolds and smooth manifolds with the same homology as $S^3\times S^5$. Some questions of Escher-Ziller are also discussed.

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for…

Let $X$ be a $2n$-manifold with a locally standard action of a compact torus $T^n$. If the free part of action is trivial and proper faces of the orbit space $Q$ are acyclic, then there are three types of homology classes in $X$: (1)…

We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…

The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case…