Related papers: Symplectic log Calabi-Yau surface---deformation cl…

In this paper we extend the classification scheme in [S] for $b^m$-symplectic surfaces and, more generally, $b^m$-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable…

We construct geometric maps from the cyclic homology groups of the (compact or wrapped) Fukaya category to the corresponding $S^1$-equivariant (Floer/quantum or symplectic) cohomology groups, which are natural with respect to all Gysin and…

There are easy "polynomial" deformations of Calabi-Yau hypersurfaces in toric varieties performed by changing the coefficients of the defining polynomial of the hypersurface. In this paper, we explicitly constructed the ``non-polynomial''…

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction $\sigma|_Y$ of the holomorphic symplectic form induces a rank one foliation on Y. We investigate situations where this foliation has compact…

We explicitly produce symplectic genus-3 Lefschetz pencils (with base points), whose total spaces are homeomorphic but not diffeomorphic to rational surfaces CP^2 # p (-CP^2) for p= 7, 8, 9. We then give a new construction of an infinite…

We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and…

This article provides the first extension of Lagrangian Intersection Floer cohomology to Poisson structures which are almost everywhere symplectic, but degenerate on a lowerdimensional submanifold. The main result of the article is the…

In this paper we construct and classify Lagrangian T^3-fibrations on non compact symplectic manifolds with singular fibres of prescribed topological type. This contributes to the understanding of the structure of the singular fibres that…

We study symplectic (contact) structures on nilmanifolds that correspond to the filiform Lie algebras - nilpotent Lie algebras of the maximal length of the descending central sequence. We give a complete classification of filiform Lie…

In this paper we show that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting several simple families of surfaces which are not deformation…

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in…

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…

In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-K\"ahler manifolds $(X,J,g,\omega)$ with $J$ $\mathcal{C}^\infty$-pure and full the space of de Rham…

Complex Ricci-flat (i.e., Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) $U(1)^n$ gauge symmetry of general type (encoded by certain non-convex and multi-layered multitopes) may degenerate, but can be smoothed by rational…

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general…

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…

We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following…

This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section. We look at the…

$A_\infty$ categories are a mathematical structure that appears in topological field theory, string topology, and symplectic topology. This paper studies the cyclic homology of a Calabi-Yau $A_\infty$ category, and shows that it is…

It is known that the union of fibers over elliptic singularities of an almost toric fibered (ATF) closed symplectic four-manifold forms a symplectic log Calabi-Yau (LCY) divisor. In this paper, we show the converse: any symplectic LCY…