The Turaev and Thurston norms
arXiv:1412.2406 · doi:10.2140/pjm.2016.284.365
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.
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