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

小行星9602950 该美洲计划奖将资助佛罗里达州立大学的Wolfgang Heil博士与墨西哥数学研究中心（CIMAT）的卡洛斯戈麦斯-拉拉纳加和维克托努涅斯博士之间的合作研究项目，以研究不可定向的三维流形。 三维流形是一种特殊的拓扑空间，局部看起来像标准的三维欧氏空间。 三维流形理论将这种流形分成两个子类：定向流形和非定向流形。 在这两个子类中，不可定向类具有独特的不同行为，并且可能比可定向类具有更丰富的结构。 为了理解这种结构，研究人员打算研究将这种流形分解为可定向的部分，并将这些分解与一个有序的三元组（trigenus）联系起来，这可能为它们的分类提供一个有用的方法。 参与合作的数学家一直处于推进三属概念的最前沿;对这项工作的支持将使他们能够将其应用于更广泛的3-流形，并在这一领域获得新的成果。 ***

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. ***