Related papers: Tautological classes and higher signatures

For the associative algebra $A(\mathfrak g)$ of an infinite-dimensional Lie algebra $\mathfrak g$, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic…

The topological fundamental group $\pi_{1}^{top}$ is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces which admit universal covers. For an arbitrary…

Let $M$ be a manifold and $\Lambda$ a compact exact connected Lagrangian submanifold of $T^*M$. We can associate with $\Lambda$ a conic Lagrangian submanifold $\Lambda'$ of $T^*(M\times R)$. We prove that there exists a canonical sheaf $F$…

Let $X$, $D$ be a smooth projective surface and a simple normal crossing divisor on $X$, respectively. Suppose $\kappa (X, K_X + D)\ge 0$, let $C$ be an irreducible curve on $X$ whose support is not contained in $D$ and $\alpha$ a rational…

Let $G$ be a compact connected Lie group and let $\xi,\nu$ be complex vector bundles over the classifying space $BG$. The problem we consider is whether $\xi$ contains a subbundle which is isomorphic to $\nu$. The necessary condition is…

We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with…

Let $X$ be a locally symmetric space $\Gamma\backslash G/K$ where $G$ is a connected non-compact semisimple real Lie group with trivial centre, $K$ is a maximal compact subgroup of $G$, and $\Gamma\subset G$ is a torsion-free irreducible…

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite…

This paper is a generalization of a previous paper by the author to connected unipotent linear algebraic groups. The notion of an $ \alpha $-pair answers when an open $ G $-stable, affine, sub-variety $ D(H) $ is a trivial bundle over $ G…

We explore a large class of F-theory compactifications to four dimensions. We find evidence that gauge groups that cannot be Higgsed without breaking supersymmetry, often accompanied by associated matter fields, are a ubiquitous feature in…

We use K-area homology to summarize some results about the Novikov conjecture and the Hirzebruch L-class. In fact, we provide necessary and sufficient conditions for closed manifolds to have a homotopy invariant L-class. In order to obtain…

Each loop $\psi$ in the group $\text{Ham}(M)$ of Hamiltonian diffeomorphisms of a symplectic manifold $M$ determines a fibration $E$ on $S^2$, whose coupling class \cite{G-L-S} is denoted by $c$. If $VTE$ is the vertical tangent bundle of…

We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint $G$-bundles of different topological types over complex curves $\Sigma_{g,n}$ of genus $g$ with $n$ marked…

Consider the infinite dimensional flag manifold $LK/T$ corresponding to the simple Lie group $K$ of rank $l$ and with maximal torus $T$. We show that, for $K$ of type $A$, $B$ or $C$, if we endow the space $H^*(LK/T)\otimes…

Let $X$ be a closed symplectic manifold equipped a Lagrangian torus fibration over a base $Q$. A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space $Y$, which can be considered as a…

In the previous paper, the author showed that for a smooth family $X \to \mathbb{X} \to B$ of a homotopy $K3$ surface, the obstruction for the tangent bundle along the fibers $T_B \mathbb{X}$ to have a spin structure is canonically…

Combings of oriented compact 3-manifolds are homotopy classes of nowhere zero vector fields in these manifolds. A first known invariant of a combing is its Euler class, that is the Euler class of the normal bundle to a combing…

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all…

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…

Using the work of Dwyer, Weiss, and Williams we associate an invariant to any topologically trivial family of smooth h-cobordisms. This invariant is called the smooth structure class, and is closely related to the higher Franz--Reidemeister…