# The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology

 Title: The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology Author: McMullen, Curtis T. Citation: McMullen, Curtis T. 2002. The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology. Annales Scientifiques de l'École Normale Supérieure 35(2): 153–171. Full Text & Related Files: alexander_polynomial.pdf (271.0Kb; PDF) Abstract: Let M be a connected, compact, orientable 3-manifold with $$b_1(M)>1$$, whose boundary (if any) is a union of tori. Our main result is the inequality $${\parallel \phi \parallel}_A \le {\parallel \phi \parallel}_T$$ between the Alexander norm on $$H^1(M,\mathbb{Z})$$, defined in terms of the Alexander polynomial, and the Thurston norm, defined in terms of the Euler characteristic of embedded surfaces. (A similar result holds when $$b_1(M)=1$$.) Using this inequality we determine the Thurston norm for most links with 9 or fewer crossings. Published Version: doi:10.1016/S0012-9593(02)01086-8 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9871964

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