相关论文: Remarks on the flux groups
We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with…
The main subjects of the paper is studying the fundamental groups of closed symplectically aspherical manifolds. Motivated by some results of Gompf, we introduce two classes of fundamental groups $\pi_1(M)$ of symplectically aspherical…
We explore the symmetry group of the pressure isotropy condition in isotropic coordinates finding a rich structure. We work out some specific examples.
Our interest in this work is in group extensions of minimal flows with compact abelian groups in the fibres. We study their structure from categorical and algebraic points of view, and describe relations of their dynamics to the…
This is mainly a survey of recent work on algebraic ways to ``measure'' moduli spaces of connecting trajectories in Morse and Floer theories as well as related applications to symplectic topology. The paper also contains some new results.…
In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…
In this survey paper, we will collate various different ideas and thoughts regarding equivariant operations on quantum cohomology (and some in more general Floer theory) for a symplectic manifold. We will discuss a general notion of…
This paper studies groups of symplectomorphisms of ruled surfaces for symplectic forms with varying cohomology class. This class is characterized by the ratio R of the size of the base to that of the fiber. By considering appropriate spaces…
We consider topological twists of four-dimensional $\mathcal{N}=2$ supersymmetric QCD with gauge group SU(2) and $N_f\leq 3$ fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which…
This is an exposition of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The original work appeared in [1].
The topology of symplectic 4-manifolds is related to that of singular plane curves via the concept of branched covers. Thus, various classification problems concerning symplectic 4-manifolds can be reformulated as questions about singular…
We consider closed symplectically aspherical manifolds, i.e. closed symplectic manifolds $(M,\omega)$ satisfying the condition $[\omega]|_{\pi_2M}=0$. Rudyak and Oprea [RO] remarked that such manifolds have nice and controllable homotopy…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
This article uses homological methods for evaluating compactly supported cohomology groups of noncompact toric surfaces
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a…
These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for…
We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…
A method of computation of its terms is presented together with some stabilization results. As an application a characterization of symplectic harmonic manifolds is given and a relationship with the C-spectral sequence is indicated.
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.