Twisted Alexander norms give lower bounds on the Thurston norm

Friedl, Stefan; Kim, Taehee

doi:10.1090/S0002-9947-08-04455-3

Twisted Alexander norms give lower bounds on the Thurston norm
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by Stefan Friedl and Taehee Kim PDF

Trans. Amer. Math. Soc. 360 (2008), 4597-4618 Request permission

Abstract:

We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number greater than one, generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many 3-manifolds which are not determined by norms of McMullen and Turaev.

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