Closed curves and geodesics with two self-intersections on the Punctured torus |
| |
| Authors: | David Crisp Susan Dziadosz Dennis J. Garity Thomas Insel Thomas A. Schmidt Peter Wiles |
| |
| Affiliation: | (1) Department of Mathematics, Flinders University, 5001 Adelaide, Australia;(2) Department of Mathematics, University of Michigan, 48109 Ann Arbor, Michigan, USA;(3) Department of Mathematics, Oregon State University, Kidder Hall 368, 97331-4605 Corvallis, Oregon, USA;(4) Department of Mathematics, University of California, 94720 Berkeley, California, USA;(5) Department of Mathematics, Oregon State University, Kidder Hall 368, 97331-4605 Corvallis, Oregon, USA;(6) Department of Mathematics, University of Wisconsin, 53706 Madison, Wisconsin, USA |
| |
| Abstract: | We classify the free homotopy classes of closed curves with minimal self intersection number two on a once punctured torus,T, up to homeomorphism. Of these, there are six primitive classes and two imprimitive. The classification leads to the topological result that, up to homeomorphism, there is a unique curve in each class realizing the minimum self intersection number. The classification yields a complete classification of geodesics on hyperbolicT which have self intersection number two. We also derive new results on the Markoff spectrum of diophantine approximation; in particular, exactly three of the imprimitive classes correspond to families of Markoff values below Hall's ray.Research started during the Summer 1994 NSF REU Program at Oregon State University and partially supported by NSF DMS 9300281 |
| |
| Keywords: | 53A35 57M50 11J06 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
