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arXiv · 2005.03414

A note on Penner's cocycle on the fatgraph complex

Yusuke Kuno·Kae Takezawa
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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.

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Yusuke Kuno, Kae Takezawa. 2020-06-01. A note on Penner's cocycle on the fatgraph complex. https://arxiv.org/abs/2005.03414

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