Related papers: Unobstructed embeddings in Hirzebruch surfaces

A smooth counterexample to the Hamiltonian Seifert conjecture for six-dimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2n-dimensional vector space, 2n > 4, such that one of…

For an infinite type surface $\Sigma$, we consider the space of (marked) convex hyperbolic structures on $\Sigma$, denoted $H(\Sigma)$, with the Fenchel-Nielsen topology. The (big) mapping class group acts faithfully on this space allowing…

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and…

We consider various trace formulas for the cubic Schrodinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian…

We give a complete obstruction to turning an immersion of an m-dimensional manifold M in Euclidean n-space into an embedding when 3n>4m+4. It is a secondary obstruction, and exists only when the primary obstruction, due to Haefliger,…

In this article we study proper symplectic and iso-symplectic embeddings of $4$--manifolds in $6$--manifolds. We show that a closed orientable smooth $4$--manifold admitting a Lefschetz fibration over $\C P^1$ admits a symplectic embedding…

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…

In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex…

Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula…

We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface $H$ in a toric variety $V$ we construct…

We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite…

We obtain new sharp obstructions to symplectic embeddings of four-dimensional polydisks $P(a,1)$ into four-dimensional ellipsoids $E(bc,c)$ when $1\le a< 2$ and $b$ is a half-integer. When $1 \leq a < 2-O(b^{-1})$ we demonstrate that…

Given a compact orientable surface with finitely many punctures $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential unoriented simple closed curves in $\Sigma$. We determine a complete set of relations for a function…

The systole of a hyperbolic surface is bounded by a logarithmic function of its genus. This bound is sharp, in that there exist sequences of surfaces with genera tending to infinity that attain logarithmically large systoles. These are…

In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface where the symplectic volume goes either to infinity or to zero…

The group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat $(1,9)$-dimensional space, whose induced metric is static and spherically symmetric. For such…

A topological condition is given, characterizing which closed manifolds in dimensions < 8 (and conjecturally in general) admit symplectic structures. The condition is the existence of a certain fibration-like structure called a hyperpencil.…

A surface in the Teichm\"uller space, where the systole function admits its maximum, is called a maximal surface. For genus two, a unique maximal surface exists, which is called the Bolza surface, whose systolic geodesics give a…

This is a collection of results on the topology of toric symplectic manifolds. Using an idea of Borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Further, the product of two projective…

Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy…