Related papers: Generalization of Weinstein's Morphism

We introduce a generalization of Weinstein's morphism, defined on \pi_{2k-1}(Ham(M,\omega)) for 1 < k \leq n, where (M,\omega) is a 2n-dimensional symplectic manifold. Using this morphism, we show that for n > 1 and 1 < k \leq n, the…

We prove that the fundamental group of the group of Hamiltonian diffeomorphisms of the symplectic manifold that is obtain by blowing up a submanifold contains an element of infinite order. We prove this using Weinstein's morphism and by…

Let $k$ be a field, let $H \subset G$ be (possibly disconnected) reductive groups over $k$, and let $\Gamma$ be a finitely generated group. Vinberg and Martin have shown that the induced morphism of character varieties \[…

We prove that $\pi_1(\text{Ham}(M))$ contains an infinite cyclic subgroup, where $\text{Ham}(M)$ is the Hamiltonian group of the one point blow up of ${\Bbb C}P^3$. We give a sufficient condition for the group $\pi_1(\text{Ham}(M))$ to…

Let $(\X,\omega)$ be a compact symplectic orbifold. We define $\pi_1(Ham(\X, \omega))$, the fundamental group of the 2-group of Hamiltonian diffeomorphisms of $(\X, \omega)$, and construct a group homomorphism from $\pi_1(Ham(\X, \omega))$…

Suppose that a finite group $G$ admits an automorphism $\varphi $ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the…

We lift a Hamiltonian loop on a symplectic manifold to a Hamiltonian loop on the symplectic one-point blow up of a symplectic manifold. Then we use Weinstein's morphism to show that the lifted Hamiltonian loop has infinite order on the…

Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group…

This paper is on the Curtis conjecture. We show that the image of the Hurewicz homomorhism $h:\pi_*Q_0S^0\to H_*(Q_0S^0;\mathbb{Z})$, when restricted to product of positive dimensional elements, is determined by…

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

A bi-invariant differential 2-form on a Lie group G is a highly constrained object, being determined by purely linear data: an Ad-invariant alternating bilinear form on the Lie algebra of G. On a compact connected Lie group these have an…

A new approach to the quantization of constrained or otherwise reduced classical mechanical systems is proposed. On the classical side, the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in…

The $\pi_2$-diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds…

For a manifold $M$ with an integral closed 3-form $\omega$, we construct a $PU(H)$-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural…

In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…

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 analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for…

Two natural symplectic constructions, the Lagrangian suspension and Seidel's quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M,\omega) a monotone symplectic manifold, admit…

Let $R$ be a commutative ring. For any projective $R$-module $P_0$ of constant rank $2$ with a trivialization of its determinant, we define a generalized Vaserstein symbol on the orbit space of the set of epimorphisms $P_0 \oplus R…