Related papers: Surjective holomorphic maps onto Oka manifolds

We prove that for any complex manifold X, the set of all holomorphic maps from the unit disc to X whose images are everywhere dense in X forms a dense subset in the space of all holomorphic maps from the disc to X. We show by an example…

We study holomorphic supercurves, which are motivated by supergeometry as a natural generalisation of holomorphic curves. We prove that, upon perturbing the defining equations by making them depend on a connection, the corresponding…

For the model two-complex $K$ of the group presentation $\mathcal{P}=\langle x,y\,|\,x^{k+1}yxy \rangle$, with $k\geq1$ odd, we describe representatives for all free and based homotopy classes of maps from $K$ into the real projective plane…

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of…

We extend Siu's and Sampson's celebrated rigidity results to non-compact domains. More precisely, let $M$ be a smooth quasi-projective variety with universal cover $\tilde M$ and let $\tilde X$ be a symmetric space of non-compact type, a…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{\xi_1,...,\xi_s\}$. We use this sequence to…

Let $M$ be a compact orientable surface equipped with a volume form $\omega$, $P$ be either $\mathbb{R}$ or $S^1$, $f:M\to P$ be a $C^{\infty}$ Morse map, and $H$ be the Hamiltonian vector field of $f$ with respect to $\omega$. Let also…

For an $\A^1$-connected pointed simplicial sheaf $\sX$ over a perfect field $k$, we prove that the Hurewicz map $\pi_1^{\A^1}(\sX) \to H_1^{\A^1}(\sX)$ is surjective. We also observe that the Hurewicz map for $\P^1_k$ is the abelianisation…

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…

In this paper we prove that for a complete, connected and oriented K\"{a}ler affine manifold $(M,G)$ of dimension $n,$ if it is K\"ahler affine Ricci flat or the K$\ddot{a}$hler affine scalar curvature $S\equiv0,$ ($n\leq 5$), then the…

Oka theory has its roots in the classical Oka principle in complex analysis. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. Following a brief review of Stein…

Let K be a subset of a smooth manifold M. In some cases functor calculus methods lead to a homotopical formula for M minus K in terms of the subspaces M minus S, where S runs through the finite subsets of K.

There exists a homomorphism from the affine super Yangian to the completion of the universal enveloping algebra of $\widehat{\mathfrak{gl}}(m|n)$, called the evaluation map. In this paper, we show that this homomorphism is surjective. Via…

Extending a result of Schr\"oer on a Grothendieck question in the context of complex analytic spaces, we prove that the surjectivity of the Brauer map $\delta: Br(X) \rightarrow H_{\rm \'et}^2(X,\mathbb{G}_{m, X})_{\rm tor}$ for algebraic…

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be K\"ahler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable…

Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certain assumptions, it can be approximated in the compact-open…

Given a closed $n$-manifold, we consider the set of simple homotopy types of $n$-manifolds within its homotopy type, called its simple homotopy manifold set. We characterise it in terms of algebraic K-theory, the surgery obstruction map,…

Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…

For a negatively curved manifold $M$ and a continuous map $\psi:\Sigma\to M$ from a closed surface $\Sigma$, we study complex submanifolds of Teichm\"uller space $\mathcal{S}\subset\mathcal{T}(\Sigma)$ such that the harmonic maps…