U.S.-Mexico Collaborative Research: Study of Geometric and Topological Structures of Foliated Manifolds

9600468 Candel美洲项目奖将支持芝加哥大学Albert Candel博士和墨西哥国立理工学院（IPN）高等数学与数学学院Raul Quiroga Barranco博士之间的合作研究。本课题的目标是研究具有不同微分几何性质的特定拓扑空间的同态。具体来说，研究人员对叶面流形感兴趣，因为叶面流形沿着叶子或横向方向有几何结构。具有这种结构的紧叶理流形可以被认为是推广关于刚性几何结构的各种定理的适当候选者，在此过程中建立了叶理的mostov - margulis型刚性结果。在这些考虑中，基群和叶理的伸展将起重要作用。＊＊＊

9600468 Candel This Americas Program award will support cooperative research between Dr. Albert Candel, University of Chicago, and Dr. Raul Quiroga Barranco of the Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, (IPN), in Mexico. The goal of this project is to study homomorphisms of specific topological spaces with various differential geometry properties. Specifically, the researchers are interested in foliated manifolds for which there are geometric structures either along the leaves or in the transverse direction. A compact foliated manifold with such structures can be considered an adequate candidate to extend various theorems concerning rigid geometric structures, establishing, in the process, Mostow-Margulis type rigidity results for foliations. In these considerations, the fundamental group and the stretch of a foliation will play an important role. ***