Geometry & Topology

Genus-two trisections are standard

Jeffrey Meier and Alexander Zupan

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Abstract

We show that the only closed 4–manifolds admitting genus-two trisections are S2 × S2 and connected sums of S1 × S3, 2 and ¯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
Received: 1 December 2014
Revised: 21 February 2016
Accepted: 25 March 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 57N12: Topology of $E^3$ and $S^3$ [See also 57M40] 57R65: Surgery and handlebodies
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
trisections Heegaard splittings waves

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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