Related papers: SL-oriented cohomology theories

This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic cohomology classes by taking pullbacks…

For a large class of cohomology theories, we prove that refined unramified cohomology is canonically isomorphic to the hypercohomology of a natural truncated complex of Zariski sheaves. This generalizes a classical result of Bloch and Ogus…

We prove the vanishing of a certain characteristic class of flat vector bundles when the structure groups of the bundles are contained in GL(N,Z). We do so by explicitly writing the characteristic class as an exact form on the base of the…

For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups…

Given two vector bundles E and F on a variety X and a morphism from Sym^2(E) to F, we compute the cohomology class of the locus in X where the kernel of this morphism contains a quadric of prescribed rank. Our formulas have many…

We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…

We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of odd order and $\Gamma$-loops of odd order. Once this…

For a finite dimensional vector space V of dimension n, we consider the incidence correspondence (or partial flag variety) X in P(V) x P(V*), parametrizing pairs consisting of a point and a hyperplane containing it. We completely…

In this paper we study some new theories of characteristic homology classes for singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformation mC_{*}: K_{0}(var/X)-> G_{0}(X)[y], which…

We construct a bigraded (co)homology theory which depends on a parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan's approach to tangles on one side, and Khovanov's sl(3) theory for…

Let $F$ and $k$ be perfect fields. The main goal of this paper is to investigate algebraic models for the Morel-Voevodsky unstable motivic homotopy category $\mathrm{Ho}(F)$ after $\mathbf{H}^{\mathbb{A}^1}k$ localization. More…

We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of the map from the ring of rational…

For a singularity type $\eta$, let the $\eta$-avoiding number of an $n$-dimensional manifold $M$ be the lowest $k$ for which there is a map $M\to\mathbb{R}^{n+k}$ without $\eta$ type singular points. For instance, the case of…

The Borel-Weil-Bott theorem describes the cohomology of line bundles over flag varieties. Here, one generalizes this theorem to a wider class of projective varieties : the wonderful varieties of minimal rank.

We prove that the cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on…

In the 1930s, H. Hopf conjectured that a closed, even-dimensional manifold of positive sectional curvature has positive Euler characteristic. We show this under the additional assumption of an isometric $T^4$-action on the manifold,…

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 $\kgl$-linear cohomology theories over an affine Dedekind scheme $S$ admit a canonical weight filtration on resolvable motives without inverting residual characteristics. Combined with upcoming work of Annala--Hoyois--Iwasa,…

We give a complete classification of Q_l-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which…

A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…