Related papers: $S^2$-bundles over 2-orbifolds

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if $\pi_1(M)'$ is perfect,…

A compact 4-dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing T^2-bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the…

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of…

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces…

A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…

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,…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order.

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We classify $T^2$-GKM fibrations in which both fiber and base are the GKM graph of $S^4$, with standard weights in the base. For each case in which the total space is orientable, we construct, by explicit clutching, a realization as a…

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…

\def\mon{S^3\stackrel{S^1}{\rightarrow}S^2} \def\inst{S^7\stackrel{S^3}{\rightarrow}S^4} \def\octo{S^{15}\stackrel{S^7}{\rightarrow}S^8} In semilocal theories, the vacuum manifold is fibered in a non-trivial way by the action of the gauge…

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an…

In this paper, we introduce the classification of equivariant principal bundles over the 2-sphere. Isotropy representations provide tools for understanding the classification of equivariant principal bundles. We consider a…

This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…

Suppose that $N_1$ and $N_2$ are closed smooth manifolds of dimension $n$ that are homeomorphic. We prove that the spaces of smooth knots $Emb(S^1, N_1)$ and $Emb(S^1, N_2)$ have the same homotopy $(2n-7)$-type. In the 4-dimensional case…

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and…

This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We…

For a manifold $M$ with an integral closed 3-form $\omega$, we construct a $PU(H)$-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural…