Related papers: Topology of symplectomorphism groups of rational r…

Let $\mathcal C$ be category over a commutative ring $k$, its Hochschild-Mitchell homology and cohomology are denoted respectively $HH_*(\mathcal C)$ and $HH^*(\mathcal C).$ Let $G$ be a group acting on $\mathcal C$, and $\mathcal C[G]$ be…

In this article we give formulas for the Riemann-Roch number of a symplectic quotient arising as the reduced space corresponding to a coadjoint orbit (for an orbit close to 0) as an evaluation of cohomology classes over the reduced space at…

Generalizing work of Doi and of Idrissi, we define a coHochschild homology theory for chain coalgebras over any commutative ring and prove its naturality with respect to morphisms of chain coalgebras up to strong homotopy. As a consequence…

Let $(G,\Omega)$ be a symplectic Lie group, i.e, a Lie group endowed with a left invariant symplectic form. If $\G$ is the Lie algebra of $G$ then we call $(\G,\omega=\Om(e))$ a symplectic Lie algebra. The product $\bullet$ on $\G$ defined…

We study the symplectomorphism groups $G_{\lambda}=Symp_0(M,\omega_{\lambda})$ of an arbitrary closed manifold M equipped with a 1-parameter family of symplectic forms $\omega_{\lambda}$ with variable cohomology class. We show that the…

Goodwillie \cite{Goodwillie} introduced a periodic cyclic homology group associated to a mixed complex. In this paper, we apply this construction to the symplectic cochain complex of a Liouville domain $M$ and obtain two periodic symplectic…

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex…

In this paper we describe a method to establish when a symplectic manifold $M$ with semi-free Hamiltonian $S^{1}$-action is unique up to isomorphism (equivariant symplectomorphism). This will rely on a study of the symplectic topology of…

Since Quillen proved his famous equivalences of homotopy categories in 1969, much work has been done towards classifying the rational homotopy types of simply connected topological places. The majority of this work has focused on rational…

We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…

An isometric compact group action $G \times (M,g) \rightarrow (M,g)$ is called polar if there exists a closed embedded submanifold $\Sigma \subseteq M$ which meets all orbits orthogonally. Let $\Pi$ be the associated generalized Weyl group.…

It is well-known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group $G$ can be detected on the cohomology group $\mathrm{H}^1(G,R[G])$, where $R$ is either a finite field, the…

Banyaga has shown that the group of symplectomorphisms Symp(N) of a compact symplectic manifold (N,w) determines the symplectic structure. This motivates the study of the homotopy properties of Symp(N). Gromov has shown that the group of…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…

We describe the Whitehead products in the rational homotopy group of a connected component of a mapping space in terms of the Andr\'{e}-Quillen cohomology. As a consequence, an upper bound for the Whitehead length of a mapping space is…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all…

The category of rational G-equivariant cohomology theories for a compact Lie group $G$ is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of…

We show that if K: P \to R is an autonomous Hamiltonian on a symplectic manifold (P,\Omega) which attains 0 as a Morse-Bott nondegenerate minimum along a symplectic submanifold M, and if c_1(TP)|_M vanishes in real cohomology, then the…