Related papers: Rationality of secondary classes

I prove the Bloch conjecture:all secondary characteristic classes of flat bundles over complex projective varietes are torsion, except the first.

We study real double covers of $\mathbb P^1\times\mathbb P^2$ branched over a $(2,2)$-divisor, which have the structure of a conic bundle threefold with smooth quartic discriminant curve via the second projection. In each isotopy class of…

We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles…

In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m-th symmetric power of…

This paper makes certain observations regarding some conjectures of Milnor and Ramakrishnan in hyperbolic geometry and algebraic K-theory. As a consequence of our observations, we obtain new results and conjectures regarding the rationality…

We show that isomorphism classes $[\mathcal{A}]$ of flat $q\times q$ matrix bundles $\mathcal{A}$ (or projectively flat rank-$q$ complex vector bundles $\mathcal{E}$) on a pro-torus $\mathbb{T}$ are in bijective correspondence with the…

We compute the equivariant $K$-homology of the classifying space for proper actions, for compact 3-dimensional hyperbolic reflection groups. This coincides with the topological $K$-theory of the reduced $C^\ast$-algebra associated to the…

Let $M(2,\textbf{\underline{w}},\chi)$ be the moduli space of rank $2$ torsion-free sheaves over a reducible nodal curve with each component having utmost two nodal singularities. We show that in each component of…

Let $\sE$ be an ample rank $r$ bundle on a smooth toric projective surface, $S$, whose topological Euler characteristic is $e(S)$. In this article, we prove a number of surprisingly strong lower bounds for $c_1(\sE)^2$ and $c_2(\sE)$. We…

We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by…

We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the…

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a…

Let $S \subset \mathbb P^3$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this…

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…

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

We show that all filtrable bundles on a Hopf surface $X$ must have jumps and we prove the existence of filtrable stable bundles on $X$ with any value of $c_2>0$. On a somewhat opposite direction, for each integer $r\ge 2$ we prove the…

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of…

If E is a C^\infty complex vector bundle on an oriented C^\infty manifold \Sigma, diffeomorphic to a circle, then the space of sections of E has a canonical polarization in the sense of Pressley and Segal and so one has its determinantal…

Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and…

We prove equality of analytic and topological $L^2$-torsion associated with an odd-dimensional finite volume hyperbolic manifold and a representation of the fundamental group which extends to the ambient Lie group. This generalizes a…