Simple Curves on Surfaces
β Scribed by Igor Rivin
- Book ID
- 110308620
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 178 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We describe an optimal algorithm to decide if one closed curve on a triangulated 2-manifold can be continuously transformed to another, i.e., if they are homotopic. Suppose C 1 and C 2 are two closed curves on a surface M of genus g. Further, suppose T is a triangulation of M of size n such that C 1
It is proved that for each compact (bordered) surface 7 and each integer k there is a constant N with the following property: If 1 is a family of pairwise nonhomotopic closed curves on 7 such that any two curves from 1 intersect in at most k points, then 1 contains at most N curves.