Mathematical Sciences: Equivariant KK Theory

该奖项支持Peter Haskell的研究（联合 与科罗拉多大学的Jeffrey Fox）关于等变的 KK理论 等变K-理论与交叉的K-理论 积代数在求解 与群作用有关的几何和拓扑问题 和流形的基本群。 的例子 问题包括Gromov-Lawson-Rosenberg的许多案例 关于正标度规存在性的一个猜想 曲率和诺维科夫猜想的许多情况下， 高阶签名的同伦不变性 卡斯帕罗夫的 表示环KK（G）（C，C）及其特征幂等元 在这个项目中发挥了重要作用。 本研究 我将应用卡斯帕罗夫表示理论， 对K理论的几何理解做出了贡献 交叉积C（*）-代数 这项“现代分析”的工作融合了复杂的研究 在代数、几何和分析中， 流形或曲面的理论。 这种分析是通过 空间变换群在曲面上的作用，或 在这个空间中的几何物体。

This award supports the research of Peter Haskell (joint with Jeffrey Fox of the University of Colorado) on equivariant KK-theory. Equivariant K-theory and the K-theory of crossed product algebras have played an important role in the solution of geometric and topological problems associated with group actions and with fundamental groups of manifolds. Examples of such problems include many cases of the Gromov-Lawson-Rosenberg conjecture on the existence of metrics with positive scalar curvature and many cases of the Novikov conjecture on the homotopy invariance of higher signatures. Kasparov's representation ring KK(G)(C,C) and its distinguished idempotent have played a fundamental role in this program. This research will apply the Kasparov representation theory with the intention for contributing to the geometric understanding of the K-theory of crossed product C(*)-algebras. This work in 'modern analysis' blends sophisticated research in algebra, geometry, and analysis to examine the underlying theory of manifolds or surfaces. This analysis is by way of the action of the transformation groups of a space on a surface or geometric object in that space.