Related papers: Whitehead-Torsion und Faserungen

Let $f\colon M\to N$ be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that $N$ is not a closed graph-manifold. Suppose that $f$ induces an epimorphism on fundamental groups. We…

Let $f:E\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \emph{$Lf-$function} $\Theta_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space…

In this paper, we consider a special relative K\"ahler fibration that satisfies a homogenous Monge-Amp\`ere equation, which is called a Monge-Amp\`ere fibration. There exist two canonical types of generalized Weil-Petersson metrics on the…

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle…

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…

Let $X$ be a complex manifold and $L$ be a holomorphic line bundle on $X$. Assume that $L$ is semi-positive, namely $L$ admits a smooth Hermitian metric with semi-positive Chern curvature. Let $Y$ be a compact K\"ahler submanifold of $X$…

In this paper we describe and continue the study begun by the author, Jones, and Segal, of the homotopy theory that underlies Floer theory. In that paper the authors addressed the question of realizing a Floer complex as the celluar chain…

Let $A$ be a diagonal linear operator on $\C^n$, with all eigenvalues satisfying $0<|\alpha_i|<1$, and $M = (\C^n\backslash 0)/<A>$ the corresponding Hopf manifold. We show that any stable holomorphic bundle on $M$ can be lifted to a…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

We present a general construction of embedded minimal and constant mean curvature surfaces in $\mathbb{S}^n$ and one-phase free boundaries joined by a smooth interpolation by capillary hypersurfaces. This framework recovers all known…

Let $X$ be a smooth projective horospherical variety of Picard number one. We show that a uniruled projective manifold of Picard number one is biholomorphic to $X$ if its variety of minimal rational tangents at a general point is…

For any integer $ p \geq 2 $, we construct a compact Riemannian manifold $ \mathcal{N} $ such that if $ \dim \mathcal{M} > p $, there is a map in the Sobolev space of mappings $ W^{1,p} (\mathcal{M}, \mathcal{N})$ which is not a weak limit…

We develop square zero obstruction theory for modules over $\mathbb{E}_1$-algebras in an arbitrary stable (presentably) monoidal $\infty$-category. We explicitly describe the obstruction element as the homotopy class of a canonically…

Using the work of Dwyer, Weiss, and Williams we associate an invariant to any topologically trivial family of smooth h-cobordisms. This invariant is called the smooth structure class, and is closely related to the higher Franz--Reidemeister…

Any two homologous surfaces of the same genus embedded in a smooth 4-manifold X with simply-connected complements are shown to be smoothly isotopic in the connected sum of X and the product of a 2-sphere with itself, if the surfaces are…

We prove that a circle bundle over a closed oriented aspherical manifold with hyperbolic fundamental group admits a self-map of absolute degree greater than one if and only if it is virtually trivial. This generalizes in every dimension the…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…

Some questions are posted at the end of Chapter 16 of Huybrechts' book 'Lectures on K3 Surfaces', concerning the bounded derived category of a K3 surface $D^b(S)$. Let $E$ be a spherical object in $D^b(S)$. The first question asks if there…

We review the geometric theory of \emp{smooth systems of smooth maps}, of \emp{smooth systems of smooth sections} of a smooth double fibred manifold and of \emp{smooth systems of smooth connections} of a smooth fibred manifold. Moreover,…

Let X be a real algebraic subset of R^n and M a smooth, closed manifold. We show that all continuous maps from M to X are homotopic (in X) to C^\infty maps. We apply this result to study characteristic classes of vector bundles associated…