Related papers: Lefschetz fibrations, complex structures and Seife…

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic $d\delta$-lemma for any such foliations with the (transverse) $s$-Lefschetz property. As transversely…

We prove that any finitely presented group can be realized as the fundamental group of a spin Lefschetz fibration over the 2-sphere. We moreover show that any admissible lattice point in the symplectic geography plane below the Noether line…

The purpose of this paper is to produce restrictions on fundamental groups of manifolds admitting good complexifications by proving the following Cheeger-Gromoll type splitting theorem: Any closed manifold $M$ admitting a good…

We study necessary and sufficient conditions for a 4-dimensional Lefschetz fibration over the 2-disk to admit a $\text{Pin}^{\pm}$-structure, extending the work of A. Stipsicz in the orientable setting. As a corollary, we get existence…

Log-symplectic structures are Poisson structures $\pi$ on $X^{2n}$ for which $\bigwedge^n \pi$ vanishes transversally. By viewing them as symplectic forms in a Lie algebroid, the $b$-tangent bundle, we use symplectic techniques to obtain…

In this article, we generalize the classification of genus one Lefschetz fibrations to genus one simplified broken Lefschetz fibrations, which have fibers of genera one and zero. We classify genus one Lefschetz fibrations over the 2-disk…

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz…

We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.

This work is devoted to the study of deformations of hyperbolic cone structures under the assumption that the lengths of the singularity remain uniformly bounded over the deformation. Given a sequence $(M_{i}%, p_{i}) $ of pointed…

In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In…

We apply spectral sequences to derive both an obstruction to the existence of $n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on…

Let $M$ be a compact, holomorphic symplectic Kaehler manifold, and $L$ a non-trivial line bundle admitting a metric of semi-positive curvature. We show that some power of $L$ is effective. This result is related to the hyperkaehler SYZ…

We study Milnor fibers and symplectic fillings of links of sandwiched singularities, with the goal of contrasting their algebro-geometric deformation theory and symplectic topology. In the algebro-geometric setting, smoothings of sandwiched…

Mitsumatsu constructed leafwise symplectic structures of certain codimension one foliations of the 5-sphere. This inspired the present author to improve his result on convergence of contact structure to foliation. We describe convergence of…

Let M be a closed, symplectic connected Riemannian manifold, f a symplectomorphism on M. We prove that if f is C1-stably weakly shadowing on M, then the whole manifold M admits a partially hyperbolic splitting.

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then its complexification has a hypercomplex structure. It is…

This is the third of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous two. Let $f:X\to S$ be a map of a smooth projective real algebraic 3-fold to a surface $S$ whose general…

Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1…

We show that the almost complex structure underlying a non-Kahler, nearly Kahler 6-manifold (in particular, the standard almost complex structure of S^6) cannot be compatible with any symplectic form, even locally.

In this paper we construct six-dimensional compact non-K\"ahler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known…