Related papers: Complex b-manifolds
If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance,…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
A holonomic D-module on a complex analytic manifoldadmits always a b-function along any submanifold. If the module is regular, itadmits also a regular b-function, that is a b-function with a condition on the order of the lower terms of the…
We consider a smooth boundary b\Omega which is q-convex in the sense that its Levi-form has positive trace on every complex q-plane. We prove that b\Omega is tangent of infinite order to the complexification of each of its submanifolds…
We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander…
A class of simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum*…
The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of…
Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…
We give an abstract definition, similar to the axioms of a Stein manifold, of a class of complex Banach manifolds in such a way that a manifold belongs to the class if and only if it is biholomorphic to a closed split complex Banach…
For a simplicial complex X on {1,2, ..., n} we define enriched homology and cohomology modules. They are graded modules over k[x_1, ..., x_n] whose ranks are equal to the dimensions of the reduced homology and cohomology groups. We…
We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and…
This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is…
In the previous papers we present a construction of the set ${\cal U}_{SBS}$ in the direct product ${\cal B}_S \times \mathbb{P} \Gamma (M, L)$ of the moduli space of Bohr - Sommerfeld lagrangian submanifolds of fixed topological type and…
It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex structures. On general grounds such D-branes (called generalized complex…
Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex associated to the bundle of the holomorphic p-forms to provide inequalities for all the Hodge numbers of a special class of irregular compact Kaehler manifolds. For…
A principal torus bundle over a complex manifold with even dimensional fiber and characteristic class of type $(1,1)$ admits a family of regular generalized complex structures (GCS) with the fibers as leaves of the associated symplectic…
Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in…
In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.