The girth of a Heegaard splitting
Geometric Topology
2007-05-23 v1
Abstract
We construct simple curves from immersed curves in the setting of handlebodies and Heegaard splittings. We define a measure of complexity we call girth for closed curves in a handlebody. We extend this complexity to Heegaard splittings and pose a conjecture about all Heegaard splittings. We prove a test case of this conjecture. Let S be a compact surface embedded in the boundary of a handlebody H. Then the minimum girth over all curves in S can be achieved by a simple closed curve. We also present algorithms to compute the girth of curves and surfaces.
Cite
@article{arxiv.math/0506558,
title = {The girth of a Heegaard splitting},
author = {Christopher Jerdonek},
journal= {arXiv preprint arXiv:math/0506558},
year = {2007}
}
Comments
Ph.D. dissertation, 73 pages, 22 figures (bitmapped EPS, as the arXiv cannot yet accept the vector-based PDF source)