A WU formula for Euler mod 2 spaces
Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds
As an application, we compute the Eells–Kuiper and t-invariants of certain cohomogeneity one manifolds that were studied by Dearricott, Grove, Verdiani, Wilking, and Ziller. In particular, we determine the diffeomorphism type of a new manifold of positive sectional curvature.
Algebra cochains and cyclic cohomology
Algebraic characteristic classes for idempotent matrices.
This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.
Algebraic cycles and vector bundles on real affine threefolds.
Algebroid nature of the characteristic classes of flat bundles
The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4], or the...
Amenable groups and Euler characteristic.
Ample Divisors on Fine Moduli Spaces on the Projective Plane.
An almost-integral universal Vassiliev invariant of knots.
An analytic proof of Novikov's theorem on rational Pontrjagin classes
An asymptotic formula for the eta invariants of hyperbolic 3-manifolds.
An Exotic Orientable 4-Manifold.
An Inequality of Chern Numbers for Open Algebraic Varieties.
An obstruction for smoothing of Gorenstein surface singularities.
Applications of the Ochanine Genus.
Asymptotic Lipschitz Cohomology and Higher Signatures.
Bogomolov instability of higher rank sheaves on surfaces in characteristic p.
Bounding automorphism groups.
Bounding Cohomology Groups of Vector Bundles on IPn.
Bounds for Chern classes of semistable vector bundles on complex projective spaces
This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on and a generalization of the presented method to r-bundles on is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.