Related papers: Toric contact geometry in arbitrary codimension
We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong symplectic fillings. We prove that Giroux torsion…
Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $\Gamma…
The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…
The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope associated with the vertex sets of matchings in the graph. In this paper, we study algebraic properties (compressedness, Gorensteinness) of the toric rings of…
We studied the closure of a complex subtorus given from an affine subspace in $\mathfrak{t}^{n} \cong \mathbb{R}^{n}$ in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then we…
I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold $S^2\times S^3$. In particular we give a…
The cobordism ring of symplectic manifolds defined by V.L. Ginzburg is shown to be isomorphic to the Pontrjagin ring of complex-oriented manifolds with free circle actions. This suggests an interpretation of the formal group law of complex…
In this paper we give a rigorous definition of cylindrical contact homology for contact $3$-manifolds that admit nondegenerate contact forms with no contractible Reeb orbits, and show that the cylindrical contact homology is an invariant of…
We construct toric manifolds of complex dimension $\geq 4$, whose orbit spaces by the action of the compact torus are not homeomorphic to simple polytopes (as manifolds with corners). These provide the first known examples of toric…
In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are…
To any graph $G$ one can associate a toric variety $X(\mathcal{P}G)$, obtained as a blowup of projective space along coordinate subspaces corresponding to connected subgraphs of $G$. The polytope of this toric variety is the graph…
In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich,…
In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.
Swartz proved that any matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a sphere. This was an unexpected extension from the oriented matroid case, but unfortunately the…
We usually think of 2-dimensional manifolds as surfaces embedded in Euclidean 3-space. Since humans cannot visualise Euclidean spaces of higher dimensions, it appears to be impossible to give pictorial representations of higher-dimensional…
We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we describe this volume form in terms of the Todd class. In the…
We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we…
A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…