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

 dc.contributor.author McMullen, Curtis T. dc.date.accessioned 2012-11-06T18:39:31Z dc.date.issued 2002 dc.identifier.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. en_US dc.identifier.issn 0012-9593 en_US dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:9871964 dc.description.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. en_US dc.description.sponsorship Mathematics en_US dc.language.iso en_US en_US dc.publisher Elsevier en_US dc.relation.isversionof doi:10.1016/S0012-9593(02)01086-8 en_US dash.license LAA dc.title The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology en_US dc.type Journal Article en_US dc.description.version Accepted Manuscript en_US dc.relation.journal Annales Scientifiques de l'École Normale Supérieure en_US dash.depositing.author McMullen, Curtis T. dc.date.available 2012-11-06T18:39:31Z

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