U.S.-Mexico Collaborative Research: Decompositions of Non-orientable 3-manifolds Into Handle-bodies

9602950万岁这个美洲计划奖将资助佛罗里达州立大学的沃尔夫冈·黑尔博士与墨西哥研究中心(CIMAT)的卡洛斯·戈麦斯-拉拉纳加和维克托·努涅斯合作研究不可定向的3-流形。三维流形是一种局部看起来像标准三维欧几里德空间的特殊拓扑空间。三维流形理论将这种流形分为两个子类：可定向流形和不可定向流形。在这两个子类中，不可定向的具有独特的不同行为，并且可能具有比定向的更丰富的结构。为了理解这种结构，研究人员打算研究这种流形分解成可定向的部分，并与这些分解关联一个有序的数字三元组，即三叉神经节，这可能为它们的分类提供有用的方法。参与合作的数学家一直站在推进三叉形概念的前沿；对这项工作的支持将使他们能够将这一概念应用于更广泛的三维流形，并在这一领域获得新的结果。***

9602950 Heil This Americas Program award will fund a collaborative research project between Drs. Wolfgang Heil, Florida State University, and Carlos Gomez-Larranaga and Victor Nunez, of the Centro de Investigaciones Matematicas (CIMAT), Mexico, to study non-orientable 3- manifolds. A 3-dimensional manifold is a particular topological space that locally looks like standard 3-dimensional Euclidean space. The theory of 3-dimensional manifolds splits such manifolds into two subclasses: orientable and non-orientable manifolds. Of the two subclasses, the non-orientable have a uniquely different behavior and possibly a richer structure than the orientable. To understand this structure, the investigators intend to study decompositions of such manifolds into orientable pieces and associate with these decompositions an ordered triple of numbers, the trigenus, that may provide a useful approach to their classification. The mathematicians involved in the collaboration have been at the forefront of advancing the trigenus concept; support for this work will allow them to apply it to a wider class of 3-manifolds and obtain new results in this area. ***