The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology

@article{McMullen2002TheAP,
  title={The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology},
  author={C. McMullen},
  journal={Annales Scientifiques De L Ecole Normale Superieure},
  year={2002},
  volume={35},
  pages={153-171}
}
  • C. McMullen
  • Published 2002
  • Mathematics
  • Annales Scientifiques De L Ecole Normale Superieure
Let M be a connected, compact, orientable 3-manifold with b1(M) > 1, whose boundary (if any) is a union of tori. Our main result is the inequality kk A ≤ kk T between the Alexander norm on H 1 (M, Z), defined in terms of the Alexan- der polynomial, and the Thurston norm, defined in terms of the Eu- ler characteristic of embedded surfaces. (A similar result holds when b1(M) = 1.) Using this inequality we determine the Thurston norm for most links with 9 or fewer crossings. 

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