Related papers: Toric actions in cosymplectic geometry
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…
The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for torus actions. The main ingredient in the proof is the microlocal…
We show that the cohomology algebra of the complement of a coordinate subspace arrangement in m-dimensional complex space is isomorphic to the cohomology algebra of Stanley-Reisner face ring of a certain simplicial complex on m vertices.…
Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions--those for which the dimension of the…
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…
Given two $2n$--dimensional symplectic ellipsoids whose symplectic sizes satisfy certain inequalities, we show that a certain map from the $n$--torus to the space of symplectic embeddings from one ellipsoid to the other induces an injective…
We study the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties and develop a new cyclic differential-graded operad, conjecturally governing the real version of the enumerative geometry of…
We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures…
Product Lagrangian tori in standard symplectic space $R^{2n}$ were classified up to symplectomorphism in [Che96]. We extend this classification to tame symplectically aspherical symplectic manifolds. We show by examples that the asphericity…
We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is…
A quasitoric manifold is a smooth 2n-manifold M^{2n} with an action of the compact torus T^n such that the action is locally isomorphic to the standard action of T^n on C^n and the orbit space is diffeomorphic, as manifold with corners, to…
We describe a contact analog of the symplectic cut construction. As an application we show that the group of contactomorphisms for a particular overtwisted contact structure on the three sphere contains countably many nonconjugate two tori.
We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is…
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…
We give a new proof of Givental's mirror theorem for toric manifolds using shift operators of equivariant parameters. The proof is almost tautological: it gives an A-model construction of the I-function and the mirror map. It also works for…
We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.
Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this paper we explore this correspondence to classify smooth lattice polytopes…
We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie…
We study $\mathrm{Spin}(7)$-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons-Hawking type ansatz that describes such geometries in terms of a symmetric $4\times4$-matrix of…