A conjectural Lefschetz formula for locally symmetric spaces

局部共形近Kähler流形的hard Lefschetz对偶性

The hard Lefschetz duality for locally conformally almost Kähler manifolds

本文证明局部共形近Kähler流形的hard Lefschetz对偶性，推广近Kähler情形，引入局部共形辛流形的hard Lefschetz条件，并给出反例。

A Lefschetz formula for higher rank

A general Lefschetz formula for the geodesic action on locally symmetric spaces is proven.

局部对称空间的 Lefschetz 公式

Lefschetz formula for locally symmetric spaces

本文针对实秩一局部对称空间引入群 $C^*$-代数 $C^*_r(G,\Gamma)$，刻画 Dirac 算子的 $K$-理论指标类，并借助 Hecke 对应得到 Hecke 算子 Lefschetz 数的显式公式。

Adiabatic limits of co-associative Kovalev-Lefschetz fibrations

We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

Scaling group flow and Lefschetz trace formula for laminated spaces with $p-$adic transversal

In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function $\hatζ(s)$ (resp. the zeta function $ζ_Y(s)$ of a smooth projective curve $Y$ over a finite field $\mathbb{F}_q$, $q=p^f$)) one could possibly associate a foliated Riemannian laminated space $(S_{\mathbb{Q}}, \mathcal{F}, g, ϕ^t)$ (resp. $(S_Y, \mathcal{F}, g, ϕ^t)$) endowed with an action of a flow $ϕ^t$ whose primitive compact orbits should correspond to the primes of $\mathbb{Q}$ (resp. $Y$). The existence of such a foliated space and flow $ϕ^t$ is still unknown except when $Y$ is an ellipt…

The prime geodesic theorem for higher rank spaces

The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.