The homology systole of hyperbolic Riemann surfaces
arXiv:1010.0358
Abstract
The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured surfaces, and is shown to fail for surfaces with a large number of cusps.
7 pages, 5 figures