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2017 A homology-valued invariant for trivalent fatgraph spines
Yusuke Kuno
Algebr. Geom. Topol. 17(3): 1785-1811 (2017). 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.

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Yusuke Kuno. "A homology-valued invariant for trivalent fatgraph spines." Algebr. Geom. Topol. 17 (3) 1785 - 1811, 2017. https://doi.org/10.2140/agt.2017.17.1785

Information

Received: 25 May 2016; Revised: 20 October 2016; Accepted: 30 October 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762601
MathSciNet: MR3677940
Digital Object Identifier: 10.2140/agt.2017.17.1785

Subjects:
Primary: 20F34, 32G15, 57N05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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