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2018 Comparing $4$–manifolds in the pants complex via trisections
Gabriel Islambouli
Algebr. Geom. Topol. 18(3): 1799-1822 (2018). DOI: 10.2140/agt.2018.18.1799

Abstract

Given two smooth, oriented, closed 4 –manifolds, M 1 and M 2 , we construct two invariants, D P ( M 1 , M 2 ) and D ( M 1 , M 2 ) , coming from distances in the pants complex and the dual curve complex, respectively. To do this, we adapt work of Johnson on Heegaard splittings of 3 –manifolds to the trisections of 4 –manifolds introduced by Gay and Kirby. Our main results are that the invariants are independent of the choices made throughout the process, as well as interpretations of “nearby” manifolds. This naturally leads to various graphs of 4 –manifolds coming from unbalanced trisections, and we briefly explore their properties.

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Gabriel Islambouli. "Comparing $4$–manifolds in the pants complex via trisections." Algebr. Geom. Topol. 18 (3) 1799 - 1822, 2018. https://doi.org/10.2140/agt.2018.18.1799

Information

Received: 24 July 2017; Revised: 4 December 2017; Accepted: 13 February 2018; Published: 2018
First available in Project Euclid: 26 April 2018

zbMATH: 06866413
MathSciNet: MR3784019
Digital Object Identifier: 10.2140/agt.2018.18.1799

Subjects:
Primary: 57M15, 57M99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 3 • 2018
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