McMullen, Curtis2012-11-062002McMullen, 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): 153–171.0012-9593http://nrs.harvard.edu/urn-3:HUL.InstRepos:9871964Let 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.en-USJournal Article2012-11-0610.1016/S0012-9593(02)01086-8