## Geometry & Topology

### Genus-two trisections are standard

#### Abstract

We show that the only closed $4$–manifolds admitting genus-two trisections are $S2 × S2$ and connected sums of $S1 × S3$, $ℂℙ2$ and $ℂℙ¯2$ 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 $S3$. As a corollary, we classify tunnel number one links with an integral cosmetic Dehn surgery.

#### Article information

Source
Geom. Topol., Volume 21, Number 3 (2017), 1583-1630.

Dates
Revised: 21 February 2016
Accepted: 25 March 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859207

Digital Object Identifier
doi:10.2140/gt.2017.21.1583

Mathematical Reviews number (MathSciNet)
MR3650079

Zentralblatt MATH identifier
1378.57031

#### Citation

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

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