English

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

R2 v1 2026-06-23T15:22:47.994Z