vix.ing · top · new · best · stats · spec

The Gromov norm of the product of two surfaces

2004/07/31 by Lewis Bowen, Jesús A. De Loera, Jesus A. de Loera +2
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Botany #Cartesian product #Combinatorics #Commutative Algebra and Its Applications #Genus #Geometry #Mathematics #Norm (philosophy) #Product (mathematics) #Pure mathematics #math.CO #math.GT #msc:52B12 #msc:57B45 #msc:57N13 #msc:57N65

paper · pdf · doi:10.1016/j.top.2004.10.007

published as Topology 44:2 (March 2005), 321-339 · The journal version contains an error that invalidates one direction of the main theorem. The present version contains an erratum, at the end, explaining this

openalex publication_date 2004/12/28 · arxiv created 2008/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We make an estimation of the value of the Gromov norm of the Cartesian product of two surfaces. Our method uses a connection between these norms and the minimal size of triangulations of the products of two polygons. This allows us to prove that the Gromov norm of this product is between 32 and 52 when both factors have genus 2. The case of arbitrary genera is easy to deduce form this one.

Citations