Related papers: Whitehead-Torsion und Faserungen

A full-homomorphism between a pair of graphs is a vertex mapping that preserves adjacencies and non-adjacencies. For a fixed graph $H$, a full $H$-colouring is a full-homomorphism of $G$ to $H$. A minimal $H$-obstruction is a graph that…

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…

In this work we prove that any unitary Sobolev $W^{1,2}$ connection of an Hermitian bundle over a 2-dimensional K\"ahler manifold whose curvature is $(1,1)$ defines a smooth holomorphic structure. We prove moreover that such a connection…

In this paper we study $\mathcal M(X)$, the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of $X$, via a map $\Psi$ from $\mathcal M(X)$ into the quotient of $K(X)=[X,BSO]$ by the action of the group of…

This is the beginning of an obstruction theory for deciding whether a map f:S^2 --> X^4 is homotopic to a topologically flat embedding, in the presence of fundamental group and in the absence of dual spheres. The first obstruction is Wall's…

This paper gives a uniform, self-contained and direct approach to a variety of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give necessary and sufficient cohomological criteria for the existence of various…

In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…

Let $T$ be a torus and $B$ a compact $T-$manifold. Goresky, Kottwitz, and MacPherson show in \cite{GKM} that if $B$ is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant…

Let $M$ be a closed 4-manifold with $\pi_2(M)\cong{Z}$. Then $M$ is homotopy equivalent to either $CP^2$, or the total space of an orbifold bundle with general fibre $S^2$ over a 2-orbifold $B$, or the total space of an $RP^2$-bundle over…

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…

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…

Let M be a closed orientable Seifert fibered 3-manifold with a hyperbolic base 2-orbifold, or equivalently, admitting a geometry modeled on H^2 \times R or the universal cover of SL(2,R). Our main result is that the connected component of…

Given a manifold M, it is natural to ask in how many ways it fibers (we mean fibering in a general way, where the base might be an orbifold -- this could be described as Seifert fibering)There are group-theoretic obstructions to the…

We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N between minimal differential graded algebras. We assume that M = Lambda V has an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are homotopic…

The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f: N --> M is an…

Let $f: M \to M$ denote a diffeomorphism of a smooth manifold $M$. Let $p$ in $M$ be its hyperbolic fixed point with stable and unstable manifolds $W_S$ and $W_U$, respectively. Assume that $W_S$ is a curve. Suppose that $W_U$ and $W_S$…

Given a link map f into a manifold of the form Q = N \times \Bbb R, when can it be deformed to an unlinked position (in some sense, e.g. where its components map to disjoint \Bbb R-levels) ? Using the language of normal bordism theory as…

Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…

Let $G$ be a compact connected Lie group and let $\xi,\nu$ be complex vector bundles over the classifying space $BG$. The problem we consider is whether $\xi$ contains a subbundle which is isomorphic to $\nu$. The necessary condition is…

Starting from Borel's description of the mod-2 cohomology of real flag manifolds, we give a minimal presentation of the cohomology ring for semi complete flag manifolds $F_{k,m}:=F(1,\ldots,1,m)$ where $1$ is repeated $k$ times. The…