## Geometry & Topology

### Bounds for the genus of a normal surface

#### Abstract

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact orientable 3–manifold in terms of the quadrilaterals in its cell decomposition — different bounds arise from varying hypotheses on the surface or triangulation. Two applications of these bounds are given. First, the minimal triangulations of the product of a closed surface and the closed interval are determined. Second, an alternative approach to the realisation problem using normal surface theory is shown to be less powerful than its dual method using subcomplexes of polytopes.

#### Article information

Source
Geom. Topol., Volume 20, Number 3 (2016), 1625-1671.

Dates
Accepted: 17 July 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858999

Digital Object Identifier
doi:10.2140/gt.2016.20.1625

Mathematical Reviews number (MathSciNet)
MR3523065

Zentralblatt MATH identifier
1350.57024

#### Citation

Jaco, William; Johnson, Jesse; Spreer, Jonathan; Tillmann, Stephan. Bounds for the genus of a normal surface. Geom. Topol. 20 (2016), no. 3, 1625--1671. doi:10.2140/gt.2016.20.1625. https://projecteuclid.org/euclid.gt/1510858999

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