The Turaev and Thurston norms

Stefan Friedl; Daniel S. Silver; Susan G. Williams

doi:10.2140/pjm.2016.284.365

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arXiv · 1412.2406

The Turaev and Thurston norms

Stefan Friedl·Daniel S. Silver·Susan G. Williams

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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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Stefan Friedl, Daniel S. Silver, Susan G. Williams. 2014-12-07. The Turaev and Thurston norms. https://doi.org/10.2140/pjm.2016.284.365

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