A note on Penner's cocycle on the fatgraph complex
Geometric Topology
2020-06-02 v2 Combinatorics
Abstract
We study a 1-cocycle on the fatgraph complex of a punctured surface introduced by Penner. We present an explicit cobounding cochain for this cocycle, whose formula involves a summation over trivalent vertices of a trivalent fatgraph spine. In a similar fashion, we express the symplectic form of the underlying surface of a given fatgraph spine.
Cite
@article{arxiv.2005.03414,
title = {A note on Penner's cocycle on the fatgraph complex},
author = {Yusuke Kuno and Kae Takezawa},
journal= {arXiv preprint arXiv:2005.03414},
year = {2020}
}
Comments
12 pages, 8 figures