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. ***
