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.
