相关论文: Symplectic surgeries and normal surface singularit…
We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…
We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various interesting symplectic surfaces in…
We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
A surgery of a real symplectic manifold $X_{\mathbb R}$ along a real Lagrangian sphere $S$ is a modification of the symplectic and real structure on $X_{\mathbb R}$ in a neigborhood of $S$. Genus 0 Welschinger invariants of two real…
We show, using standard results in length spectrum rigidity and symplectic homology, that if the unit tangent bundles of two compact surfaces of negative curvature are exact symplectomorphic, then the underlying surfaces are isometric, and…
We provide an infinite family of diffeomorphic symplectic forms on ruled surfaces, which are pairwise non-isotopic. This answers a uniqueness question regarding symplectic structures up to isotopy on closed symplectic four-manifolds.
We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.
For a smooth map $f:X^4\to\Sigma^2$ that is locally modeled by holomorphic maps, the domain is shown to admit a symplectic structure that is symplectic on some regular fiber, if and only if $f^*[\Sigma]\ne0$. If so, the space of symplectic…
The rational homology balls $B_n$ appeared in Fintushel and Stern's rational blow-down construction [FS2]. Later, Symington [Sy1], defined this operation in the symplectic category. In [Kh2], the author defined the inverse procedure, the…
We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this…
We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of…
We present a handlebody construction of small symplectic caps, and hence of small closed symplectic 4-manifolds. We use this to construct handlebody descriptions of symplectic embeddings of rational homology balls in…
We show that the natural symplectic structure on the Milnor fiber of an isolated singularity in complex three variables whose link fibers over the circle can be modified into one which is cylindrical at the end. As a consequence we see that…
The aim of this work is the study of symplectic structures on 2-step nilmanifolds. We concentrate in the closeness condition, proving that the existence of a closed 2-form of type II is necessary to get a symplectic structure. In low…
We consider the canonical contact structures on links of rational surface singularities with reduced fundamental cycle. These singularities can be characterized by their dual resolution graphs: the graph is a tree, and the weight of each…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional…
Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…
In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e.\ automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group schemes $\mu_{n}$ on K3…