Related papers: Obstructions to stably fibering manifolds

We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and K-homology. We propose a definition of Type II string theory on such backgrounds that further carry stratified systems…

We construct a map from the suspension $G$-spectrum $\Sigma_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism…

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor…

In the present paper we study index theory for families of manifold with corners. In particular the K-theoretical obstruction for an elliptic operator to have a family (Fredholm) index. For codimension 1 corners (families with boundary) it…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions.…

Let $X^\bullet$ be a cosimplicial object in a pointed $\infty$-category. We show that the fiber of $\mathrm{Tot}_m(X^\bullet) \to \mathrm{Tot}_n(X^\bullet)$ depends only on the pointed cosimplicial object $\Omega^k X^\bullet$ and is in…

We study the problem of existence and uniqueness of homotopy colimits in stable representation theory, where one typically does not have model category structures to guarantee that these homotopy colimits exist or have good properties. We…

Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney…

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles…

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of…

Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond…

This paper concerns extension of maps using obstruction theory under a non classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about…

We use obstruction theory based on the unstable Adams spectral sequence to construct self maps of finite quaternionic projective spaces. As a result, a conjecture of Feder and Gitler regarding the classification of self maps up to homology…

This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and show…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…

We use a recently proposed formulation of stable holomorphic vector bundles $V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to…

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

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…

In this paper, we develop the theory of singular hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold $X$ with pseudo-effective tangent bundle: $X$ admits a smooth fibration $X \to Y$…

We extend the Siu--Beauville theorem to a certain class of compact Kaehler--Weyl manifolds, proving that they fiber holomorphically over hyperbolic Riemannian surfaces whenever they satisfy the necessary topological hypotheses. As…