Related papers: The geometry of marked contact Engel structures

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…

I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I…

Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact…

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic $d\delta$-lemma for any such foliations with the (transverse) $s$-Lefschetz property. As transversely…

The space Loc(m,S) of rank m flat bundles on a closed surface S is K_2-symplectic. A threefold M bounding S gives rise a K_2-Lagrangian in Loc(m,S) given by the flat bundles on S extending to M. We generalize this, replacing the zero…

We study relations in the Grothendieck ring of varieties which connect the Hilbert scheme of points on a cubic hypersurface $Y$ with a certain moduli space of twisted cubic curves on $Y$. These relations are generalizations of the…

We show that if a manifold M admits a contact structure, then so does M\times S^2. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if M admits a contact structure then…

Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2,…

Let $(M,\omega)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion…

We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence…

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…

We study manifolds endowed with mixed metric 3--contact structures, proving that the distribution spanned by the Reeb vector fields is integrable, with totally geodesic integral manifolds, of constant sectional curvature $k=\pm1$. We also…

This paper is devoted to the systematic investigation of the cone construction for Riemannian $G$ manifolds M, endowed with an invariant metric connection with skew torsion $\nabla^c$, a `characteristic connection'. We show how to define a…

It is known that the folded sum of two contact mapping tori whose fibers are compact exact symplectic manifolds having a common convex boundary (called the ``fold'') admits a cooriented contact structure compatible with the obvious…

We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a $G_2$ structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the…

We prove every oriented compact cyclic $3$-orbifold has a contact structure. There is another proof in the web by Daniel Herr in his uploaded thesis which depends on open book decompositions, ours is independent of that. We define…

In this paper we study finite monoids M such that the group algebras over a domain R for all Schutzenberger groups of M are cell algebras. We show that for any such M the monoid algebra A over R has a standard cell algebra structure. Using…

We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build…

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle…

Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S, together with a choice of `decoration' at each component of…