相关论文: From Morse Functions to Lefschetz Fibrations on Co…

For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…

We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted…

The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some linear symmetric connection on the base space is considered. A global construction of the symplectic homogeneous connection on the…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

Given a Hopf fibration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range, the unique Lipschitz constant minimizer in its homotopy class. Similarly,…

Let $G$ be a compact and connected Lie group. The Hamiltonian $G$-model functor maps the category of symplectic representations of closed subgroups of $G$ to the category of exact Hamiltonian $G$-actions. Based on previous joint work with…

We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of…

Consider a compact K\"ahler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this…

We show that under appropriate hypotheses, a plumbing of symplectic surfaces in a symplectic 4-manifold admits strongly convex neighborhoods. Moreover the neighborhoods are Lefschetz fibered with an easily-described open book on the…

We study Hodge bundles on Siegel varieties and their various extensions to smooth toroidal compactifications. Precisely, we construct a canonical Hodge bundle on an arbitrary Siegel variety so that the holomorphic tangent bundle can be…

We investigate the Weak Lefschetz Properties for modules whose minimal free resolutions are given by generalized Kosuzl complexes in dimension three through a careful study of their Betti numbers and the symmetry and unimodality of their…

In this paper, we study compact convex Lefschetz fibrations on compact convex symplectic manifolds (i.e., Liouville domains) of dimension $2n+2$ which are introduced by Seidel and later also studied by McLean. By a result of Akbulut-Arikan,…

Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class…

The broken genera are orientation preserving diffeomorphism invariants of closed oriented 4-manifolds, defined via broken Lefschetz fibrations. We study the properties of the broken genera invariants, and calculate them for various…

Lefschetz fibration is the symplectic analogue of stable holomorphic fibration in complex geometry. A 4-dimensional stable holomorphic fibration satisfies the famous Parshin-Arakelov inequality. In this note we present an analogous…

Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…

We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent…

Let $X$ be a smooth projective variety acted on by a reductive group $G$. Let $L$ be a positive $G$-equivariant line bundle over $X$. We use the Witten deformation of the Dolbeault complex of $L$ to show, that the cohomology of the sheaf of…

We define Lie and Courant algebroids on Fr\'{e}chet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fr\'{e}chet manifold and show that it inherits a Fr\'{e}chet Lie algebroid structure. We show…

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a…