Geometric Construction of Functional Equations and Bloch Elements

[9704353] Yang这个项目涉及几何拓扑学和数论之间的接口研究。更具体地说，研究者是研究经典多对数的泛函方程，并将其与格拉斯曼多对数联系起来；探讨了代数k理论中双曲3-流形与Bloch群的密切关系。要解决的一个重要问题是用双曲流形实现Bloch群中的元素-这个问题的解决方案直接关系到K3刚性猜想。双曲3-流形通常是三维流形或弯曲空间的重要组成部分。这些是非欧几里德平面几何的负弯曲空间的推广。许多双曲3-流形可以通过某些离散对称群作为标准“平坦”双曲三维空间的商给出，这一观察结果允许研究者使用代数技术来研究双曲3-流形。

9704353 Yang This project deals with research at the interface between geometric topology and number theory. More specifically, the investigator is to study the functional equations of the classical polylogarithms and to relate this to the grassman polylogarithms; and to investigate the close relationship between hyperbolic 3-manifolds and the Bloch group in algebraic K-theory. One important question to be addressed is the realization of elements in Bloch group by hyperbolic manifolds - a solution to this question has a direct bearing on the K3 rigidity conjecture. Hyperbolic 3-manifolds are important building blocks of three-dimensional manifolds or curved spaces in general. These are negatively curved spaces generalizing the non-Euclidean plane geometries. Many hyperbolic 3-manifolds can be given as quotients of the standard 'flat' hyperbolic three space by certain discrete symmetry groups, and this observation allows researchers to use algebraic techniques to study hyperbolic manifolds.