Related papers: On holomorphic maps and Generalized Complex Geomet…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

We show that there exists a unique possible definition, with certain natural properties, of the multiple point space of a holomorphic map between complex manifolds. Our construction coincides with the double point space and the k-th…

We introduce the notion of Hamiltonian spaces for Manin pairs over manifolds, using the so-called generalized Dirac structures. As an example, we describe Hamiltonian spaces of a quasi-Lie bialgebroid using this general framework. We also…

Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…

We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…

We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in…

In this work, we obtained separation results via codimension-1 maps to generalized manifolds. More specifically, we proved results that allow us to estimate the number of connected components of the complement of the image of such maps.

We define generalised higher Whitehead maps between polyhedral products. By investigating the interplay between the homotopy-theoretic properties of polyhedral products and the combinatorial properties of simplicial complexes, we describe…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…

The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…

We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we…

Simplicial formal maps were introduced in the first paper, (math.QA/0512032), of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a…

A generalized complex manifold is locally gauge-equivalent to the product of a holomorphic Poisson manifold with a real symplectic manifold, but in possibly many different ways. In this paper we show that the isomorphism class of the…

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert…

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…

We give a new characterization of generalized K\"ahler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial unobstructedness for holomorphic Poisson structures. Our main…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…

After an elementary presentation of the relation between supersymmetric nonlinear sigma models and geometry, I focus on 2D and the target space geometry allowed when there is an extra supersymmetry. This leads to a brief introduction to…