Related papers: Holomorphic fiber bundle with Stein base and Stein…

In the present paper we consider a special class of locally trivial bundles with fiber a matrix algebra. On the set of such bundles over a finite $CW$-complex we define a relevant equivalence relation. The obtained stable theory gives us a…

We prove that a meromorphic map defined on the complement of a compact subset of a three-dimensional Stein manifold M and with values in a compact complex three-fold X extends to the complement of a finite set of points. If X is simply…

Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex…

The scope of the paper is threefold. First, we build on recent work by Hayden to compute Hedden's tau-invariant $\tau_{\xi}(L)$ in the case when $\xi$ is a Stein fillable contact structure on a rational homology sphere, and $L$ is a…

In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…

We show that the manifold $X=S^2\times S^3$ has infinitely many structures of a fiber bundle over the base $B=S^2.$ In fact for every lens space $L(p,1)$ there is a fibration $L(p,1)\to X\to B.$

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…

A contact metric manifold is said to be $H$-contact, if the characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold $M$ equipped with the standard contact metric structure is $H$-contact if…

This paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure. We show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with (continuously varying)…

A topological space (not necessarily simply connected) is said to have finite homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from the second homotopy group onward) is finite. In this article, we consider Stein…

An open subset U of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if U is homeomorphic to the interior of a handlebody whose handles all have index equal or…

For a smooth map $f:X^4\to\Sigma^2$ that is locally modeled by holomorphic maps, the domain is shown to admit a symplectic structure that is symplectic on some regular fiber, if and only if $f^*[\Sigma]\ne0$. If so, the space of symplectic…

Let X be a Stein manifold, and let Y be a closed complex submanifold of X. Denote by O(X) the algebra of holomorphic functions on X. We show that the weak (i.e., flat) homological dimension of O(Y) as a Fr'echet O(X)-module equals the…

Let $S$ be a closed oriented surface of genus $g\geq 2$. Fix an arbitrary non-elementary representation $\rho\colon\pi_1(S)\to {\rm SL}_2(\mathbb{C})$ and consider all marked (complex) projective structures on $S$ with holonomy $\rho$. We…

This is a survey on the homotopy principle in complex analysis on Stein manifolds, also called the Oka principle in this context. We concentrate on the following topics: the Oka-Grauert principle (classification of holomorphic vector…

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…

R. Guralnick [Linear Algebra Appl. 99, 85-96 (1988)] proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. In the preprints…

For a Poincare duality space X and a map X -> B, consider the homotopy fiber product X x^B X. If X is orientable with respect to a multiplicative cohomology theory E, then, after suitably regrading, it is shown that the E-homology of X x^B…

The Hitchin morphism is a map from the moduli space of Higgs bundles $\mathscr{M}_X$ to the Hitchin base $\mathscr{B}_X$, where $X$ is a smooth projective variety. When $X$ has dimension at least two, this morphism is not surjective in…

Is a given map between compact topological manifolds homotopic to the projection map of a fiber bundle? In this paper obstructions to this question are introduced with values in higher algebraic K-theory. Their vanishing implies that the…