Related papers: Homogeneous Symplectic Spaces and Central Extensio…

The Hilbert-Smith conjecture states, for any connected topological manifold $M$, any locally compact subgroup of $\mathrm{Homeo}(M)$ is a Lie group. We generalize basic results of Segal-Kosniowski-tomDieck (2.6), James-Segal (2.12), G…

We prove that a conical symplectic variety with maximal weight 1 is isomorphic to one of the following: (i) an affine space with the standard symplectic form (ii) a nilpotent orbit closure of a complex semisimple Lie algebra with the…

To the integral symplectic group Sp(2g,Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the…

This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open…

We study the homotopy type of spaces of commuting elements in connected nilpotent Lie groups, via almost commuting elements in their Lie algebras. We give a necessary and sufficient condition on the fundamental group of such a Lie group $G$…

This paper studies wavelet coorbit spaces on disconnected local fields $K$, associated to the quasi-regular representation of $G = K \rtimes K^*$ acting on $L^2(K)$. We show that coorbit space theory applies in this context, and identify…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

Let $(M,\omega)$ be a closed symplectic manifold and $\textup{Ham}(M,\omega)$ the group of Hamiltonian diffeomorphisms of $(M,\omega)$. Then the Seidel homomorphism is a map from the fundamental group of $\textup{Ham}(M,\omega)$ to the…

A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…

In this note we prove that the space of linear anti-symplectic involutions is the homogenous space $Gl(n,\R)\Sp(n)$. This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem.

We prove that every non-degenerate Reeb flow on a closed contact manifold $M$ admitting a strong symplectic filling $W$ with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive…

Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional…

We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-1)-space. Namely, for any subgroup H of G, we show that H is…

Let $(X,\omega)$ be an integral symplectic manifold and let $(L,\nabla)$ be a quantum line bundle, with connection, over $X$ having $\omega$ as curvature. With this data one can define an induced symplectic manifold $(\widetilde…

In this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is…

The key ingredient of this paper is the universal central extension of the generalized orthosymplectic Lie superalgebra $\mathfrak{osp}_{m|2n}(R,{}^-)$ coordinatized by a unital associative superalgebra $(R,{}^-)$ with superinvolution. Such…

We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V…