Geometry & Topology
- Geom. Topol.
- Volume 21, Number 3 (2017), 1583-1630.
Genus-two trisections are standard
We show that the only closed –manifolds admitting genus-two trisections are and connected sums of , and with two summands. Moreover, each of these manifolds admits a unique genus-two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus-two Heegaard diagrams of . As a corollary, we classify tunnel number one links with an integral cosmetic Dehn surgery.
Geom. Topol., Volume 21, Number 3 (2017), 1583-1630.
Received: 1 December 2014
Revised: 21 February 2016
Accepted: 25 March 2016
First available in Project Euclid: 16 November 2017
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Meier, Jeffrey; Zupan, Alexander. Genus-two trisections are standard. Geom. Topol. 21 (2017), no. 3, 1583--1630. doi:10.2140/gt.2017.21.1583. https://projecteuclid.org/euclid.gt/1510859207