Related papers: A secondary Chern-Euler class

We provide a construction of a new class of axisymmetric extremal isolated horizons admitting a structure of U(1)-principal fiber bundle over a two-sphere. In contrast to the previous examples, the null generators are assumed to be…

We present a local combinatorial formula for the Euler class of a $n$-dimen\-si\-onal PL spherical fiber bundle as a rational number $e_{\it CH}$ associated to a chain of $n+1$ abstract subdivisions of abstract $n$-spherical PL cell…

We use the compactified twistor correspondence for the (2+1)-dimensional integrable chiral model to prove a conjecture of Ward. In particular, we construct the correspondence space of a compactified twistor fibration and use it to prove…

Let G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We construct cocycles representing the generator of this group, known…

The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown…

This paper focuses on the study of a new category of vector bundles. The objects of this category, called chiral vector bundles, are pairs given by a complex vector bundle along with one of its automorphisms. We provide a classification for…

We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product $C^n$ of a curve $C = \PP^1 or \HH$: the existence of a semispecial tensor $\omega$. A…

We study the rank stratification for the differential of a Lagrangian fibration over a smooth basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As a consequence, we prove some of the vanishing, in the…

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This…

First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian…

In this paper, we prove that a compact K\"ahler manifold $X$ with the nef anti-canonical bundle $-K_{X}$ admits a locally trivial fibration $\phi \colon X \to Y$, where the fiber $F$ is a rationally connected manifold and the base $Y$ is a…

We study an asymptotic behavior of the second Chern forms of canonical metrics on a degenerating family of K\"ahler surfaces with the central fibre having ADE-singularities. We investigate a function on the unit disc defined by fiber…

Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of…

The knot quandle is a complete invariant for oriented classical knots in the $3$-sphere up to orientation. Eisermann computed the second quandle homology group of the knot quandle and showed that it characterizes the unknot. In this paper,…

Assume that $X$ is a compact complex analytic variety which has quotient singularities in codimension 2, and that $\mathcal{F}$ is a reflexive sheaf on $X$. Using orbifold modifications, we can define first and second homological Chern…

I review the dark energy solutions by a very light pseudoscalar called "quintessential axion". For the explicit breaking terms, we consider both the global anomaly U(1)$_{\rm global}\times$SU(2)$_W^2$ and the potential $\Delta V$. At the…

Here we consider higher Chern classes of vector bundles of conformal blocks on $\overline{\operatorname{M}}_{0,n}$, giving explicit formulas for them, and extending various results that hold for first Chern classes to them. We use these…

For a hermitian line bundle over an arithmetic variety, we construct a convex continuous function on the Okounkov body associated to the generic fibre of the line bundle. The integration of the continuous function gives the growth of the…

We engineer U(1)^n Chern-Simons type theories describing fractional quantum Hall solitons (QHS) in 1+2 dimensions from M-theory compactified on eight dimensional hyper-K\"{a}hler manifolds as target space of N=4 sigma model. Based on…

We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…