Related papers: Classification of equivariant vector bundles over …

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern…

In this paper we study ACM vector bundles $\E$ of rank $k \geq 3$ on hypersurfaces $X_r \subset\Pj^4$ of degree $r \geq 1$. We consider here mainly the case of degree $r = 4$, which is the first unknown case in literature. Under some…

In their construction of the topological index for flat vector bundles, Atiyah, Patodi and Singer associate to each flat vector bundle a particular $\mathbb{C/Z}$-$K$-theory class. This assignment determines a map, up to weak homotopy, from…

We apply Weiss calculus to compute the number of topological complex vector bundles of rank $n-2$ with vanishing Chern classes over $\mathbb{C}P^n$ for $n>3$, as given by the list $1, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4,…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

In this paper, we study upper bounds for the topological complexity of the total spaces of some classes of fibre bundles. We calculate a tight upper bound for the topological complexity of an $n$-dimensional Klein bottle. We also compute…

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) ($\mathbb{C}P^2\sharp\mathbb{C}P^2$)-bundle type quasitoric manifolds are weakly equivariantly…

We prove that every topological/smooth $\T=(\C^{*})^{n}$-equivariant vector bundle over a topological toric manifold of dimension $2n$ is a topological/smooth Klyachko vector bundle in the sense of arXiv:2504.02205.

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the…

We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles. For R the 3-local…

We classify the total spaces of bundles over the four sphere with fiber a three sphere up to orientation preserving and reversing homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…

This paper generalizes Bismut's equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a…

We examine several classes of manifolds which have the same cohomology ring as an Eschenburg space (a family of biquotients which is a main source of manifolds with positive curvature). One family are the 3-sphere bundles over CP^2. Another…

We show that every orbispace satisfying certain mild hypotheses has 'enough' vector bundles. It follows that the K-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth…

We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or…

We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex…