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

The main goal of this article is to construct some geometric invariants for the topology of the set $\mathcal{F}$ of flat connections on a principal $G$-bundle $P\,\longrightarrow\, M$. Although the characteristic classes of principal…

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…

We classify $5$-manifolds with fundamental group $\mathbb Z$ and $\pi_{2}$ a finitely generated abelian group in terms of the cup product on the second cohomology of the universal covering. The classification result is applied to study…

In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…

For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the…

The singular set of a generic map $f: M\to F$ of a manifold $M$ of dimension $m\ge 2$ to an oriented surface $F$ is a closed smooth curve $\Sigma(f)$. We study the parity of the number of components of $\Sigma(f)$. The image $f(\Sigma)$ of…

Let $X$ be a smooth projective curve of genus $g \geq 3$, and let $G$ be a nontrivial connected reductive affine algebraic group over $\mathbb{C}$. Examining the moduli spaces of regularly stable $G$-Higgs bundles and holomorphic…

We make the category BGrb_M of bundle gerbes on a manifold M into a 2-category by providing 2-cells in the form of transformations of bundle gerbe morphisms. This description of BGrb_M as a 2-category is used to define the notion of a…

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5 for some…

On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs…

The complement of the codimension 2 complex coordinate subspace arrangement is shown to be homotopy equivalent to a wedge of spheres.

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…

The question of whether a given H-space X is, up to homotopy, a loop space has been studied from a variety of viewpoints. Here we address this question from the aspect of homotopy operations, in the classical sense of operations on homotopy…

In this paper we discuss the topology of the symplectomorphism group of a product of two 2-dimensional spheres when the ratio of their areas lies in the interval (1,2]. More precisely we compute the homotopy type of this symplectomorphism…

We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of sections of a certain fibre bundle over M…

We study geometrical aspects of the space of fibrations between two given manifolds M and B, from the point of view of Frechet geometry. As a first result, we show that any connected component of this space is the base space of a…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…

We obtain smooth M-theory solutions whose geometry is a warped product of AdS_5 and a compact internal space that can be viewed as an S^4 bundle over S^2. The bundle can be trivial or twisted, depending on the even or odd values of the two…

We derive the $s$-invariants of certain simply connected $7$-manifolds whose second homology groups are isomorphic to $\mathbb{Z}^{2}$. We apply the $s$-invariants to give a partial classification of simply connected total spaces of circle…

We propose a geometric object slightly subtler than a complex line bundle with connection, a two-sphere fibration with structure group $\Omega^2_e S^2$, to parametrize a space of dimensional regularizations in the metaphysics of…