Related papers: Invariants of real vector bundles

In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes…

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…

Manifolds with boundary and with corners form categories ${\bf Man}\subset{\bf Man^b}\subset{\bf Man^c}$. A manifold with corners $X$ has two notions of tangent bundle: the tangent bundle $TX$, and the b-tangent bundle ${}^bTX$. The usual…

The characteristic rank of a vector bundle $\xi$ over a finite connected $CW$-complex $X$ is by definition the largest integer $k$, $0\leq k\leq \mathrm{dim}(X)$, such that every cohomology class $x\in H^j(X;\mathbb Z_2)$, $0\leq j\leq k$,…

By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted by the canonical $\mathrm{Spin}^c$…

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

We exhaustively classify topological equivariant complex vector bundles over two-torus under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) six…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

The paper combines several fortunate mini miracles to achieve its two objectives. These were woven together in a several year's effort to answer a question raised by Iz Singer a decade ago. Our answer is accessible to the topologist, to the…

Given a locally maximal compact invariant hyperbolic set $\Lambda$ for a $C^1$ flow or diffeomorphism on a Riemann manifold with $C^1$ unstable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable…

The cobordism invariance of the index on closed manifolds is reproved using the calculus of cusp pseudodifferential operators on a manifold with boundary. More generally, on a compact manifold with corners, the existence of a symmetric cusp…

We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with $c_1\leq 2$ and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated…

The aim of this note is to exhibit explicit sufficient criteria ensuring bigness of globally generated, rank-$r$ vector bundles, $r \geqslant 2$, on smooth, projective varieties of even dimension $d \leqslant 4$. We also discuss connections…

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 show that knowledge of the source-to-solution map for the fractional Dirac operator acting over sections of a Hermitian vector bundle over a smooth closed connencted Riemannian manifold of dimension $m\geq 2$ determines uniquely the…

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a…

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

We develop strong lower bounds for the span of the projective Stiefel manifolds $X_{n,r}=O(n)/(O(n-r)\times \mathbb Z/2)$, which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves…

Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume.

We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of…