A homology-valued invariant for trivalent fatgraph spines

Kuno, Yusuke

doi:10.2140/agt.2017.17.1785

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A homology-valued invariant for trivalent fatgraph spines

Yusuke Kuno

Algebraic & Geometric Topology 17 (2017) 1785–1811

DOI: 10.2140/agt.2017.17.1785

Abstract

We introduce an invariant for trivalent fatgraph spines of a once-bordered surface, which takes values in the first homology of the surface. This invariant is a secondary object coming from two 1–cocycles on the dual fatgraph complex, one introduced by Morita and Penner in 2008, and the other by Penner, Turaev and the author in 2013. We present an explicit formula for this invariant and investigate its properties. We also show that the mod 2 reduction of the invariant is the difference of two naturally defined spin structures on the surface.

Keywords

fatgraphs, Teichmüller space, Johnson homomorphism, spin structures

Mathematical Subject Classification 2010

Primary: 20F34, 32G15, 57N05

References

Publication

Received: 25 May 2016

Revised: 20 October 2016

Accepted: 30 October 2016

Published: 17 July 2017

Authors

Yusuke Kuno
Department of Mathematics Tsuda College 2-1-1 Tsuda-Machi Kodaira-shi Tokyo 187-8577 Japan

Volume 17, issue 3 (2017)