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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A homology-valued invariant for trivalent fatgraph spines

Yusuke Kuno

Algebraic & Geometric Topology 17 (2017) 1785–1811
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