The Turaev and Thurston norms

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Abstract

In 1986, W. Thurston introduced a (possibly degenerate) norm on the first cohomology group of a 3-manifold. Inspired by this definition, Turaev introduced in 2002 a analogous norm on the first cohomology group of a finite 2-complex. We show that if N is the exterior of a link in a rational homology sphere, then the Thurston norm agrees with a suitable variation of Turaev's norm defined on any 2-skeleton of N.

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Publication date Created: 2014-12-07

Publication date Updated: 2016-02-23

Article

DOI: 10.2140/pjm.2016.284.365

ArXiV ID: 1412.2406

SO-VID: 8526ea30-215b-4f8a-ae6a-c7e2cd967d68

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Comments 17 pages. V2: We deleted one direction of Lemma 4.5 since the proof was incorrect. This does not affect any of the other results of the paper

Categories math.GT

ScienceOpen disciplines: Geometry & Topology

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ScienceOpen disciplines: Geometry & Topology

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