Lefschetz-Pontrjagin Duality for Differential Characters

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。

Chern-Gauss-Bonnet and Lefschetz Duality from a currential point of view

We use the mapping cone for the relative deRham cohomology of a manifold with boundary in order to show that the Chern-Gauss-Bonnet Theorem for oriented Riemannian vector bundles over such manifolds is a manifestation of Lefschetz Duality in any of the two embodiments of the latter. We explain how Thom isomorphism fits into this picture, complementing thus the classical results about Thom forms with compact support. When the rank is odd, we construct, by using secondary transgression forms introduced here, a new closed pair of forms on the disk bundle associated to a vector bundle, pair which …

等距流的硬莱夫谢茨性质

Hard Lefschetz Property for Isometric Flows

本文将硬莱夫谢茨性质的两个版本从K-contact流推广到等距流范畴，证明二者等价，并通过具体例子说明其适用范围。

The de Rham-Federer Theory of Differential Characters and Character Duality

The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. A multiplication of de Rham-Federer characters is defined using transversality results for flat and rectifiable currents. There is a natural equivalence of ring functors from deRham - Federer characters to Cheeger-Simons characters. Differential characters have a topology and nat…

凸 valuations 的硬 Lefschetz 定理与 Hodge-Riemann 关系

Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations

本文证明了凸体上光滑平移不变 valuations 的硬 Lefschetz 定理和 Hodge-Riemann 关系，并由此得到 McMullen 二次不等式对光滑严格正曲率边界凸体的成立。