Related papers: Dalian notes on rational Pontryagin classes

It is known that in the integral cohomology of BSO(2m), the square of the Euler class is the same as the Pontryagin class in degree 4m. Given that the Pontryagin classes extend rationally to the cohomology of BSTOP(2m), it is reasonable to…

We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with fiber R^n. This amounts to an alternative proof of Novikov's theorem on the topological invariance of the rational Pontryagin classes…

We find a complete set of relations for the rational cohomology ring of the moduli space of rank three stable bundles over a Riemann surface of genus g and also show that the Pontryagin ring vanishes in degree 12g-8 and greater. The results…

The cohomology of the moduli spaces of stable bundles M(n,d), of coprime rank n and degree d, over a Riemann surface (of genus g > 1) have been intensely studied over the past three decades. We prove in this paper that the Pontryagin ring…

Given a simply connected manifold $M$, we completely determine which rational monomial Pontryagin numbers are attained by fiber homotopy trivial $M$-bundles over the $k$-sphere, provided that $k$ is small compared to the dimension of $M$.…

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows…

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used…

We study the problem of rationality of an infinite series of components, the so-called Ein components, of the Gieseker-Maruyama moduli space $M(e,n)$ of rank 2 stable vector bundles with the first Chern class $e=0$ or -1 and all possible…

Let M be a moduli space of stable vector bundles on a curve with rank and degree fixed and coprime. We give a simple proof that the rational cohomology of M is generated by the Kunneth components of the Chern classes of the universal…

We construct characteristic classes of smooth (Hamiltonian) fibrations as as fiber integrals of products of Pontriagin (or Chern) classes of vertical vector bundles over the total space of the universal fibration. We give explicit formulae…

We prove several finiteness results for the class $M_{a,b,G,n}$ of $n$-manifolds that have fundamental groups isomorphic to $G$ and that can be given complete Riemannian metrics of sectional curvatures within $[a,b]$ where $a\le b<0$. In…

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\PP$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. Such facts are used to prove…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

We show that the topological Pontryagin classes are algebraically independent in the rationalised cohomology of BTop(d) for all $d \geq 4$.

The purpose of this paper is to both survey and offer some new results on the non-triviality of the characteristic classes of Riemannian foliations. We give examples where the primary Pontrjagin classes are all linearly independent. The…

By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre $D^{2n}\sharp(S^n\times S^n)^{\sharp g}$, relative to the boundary, are for $2n\ge 6$ independent of $g$ in…

The goal of this paper is to construct universal cohomology classes on the moduli space of stable bundles over a curve when it is not a fine moduli space, i.e. when the rank and degree are not coprime. More precisely, we show that certain…

Let $Y$ be a smooth, projective curve of genus $g\geq 1$ over the complex numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings $p:X \to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy group equal…