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- W2951237014 abstract "For a 3-manifold M, McMullen derived from the Alexander polynomial of M a norm on H^1(M, R) called the Alexander norm. He showed that the Thurston norm on H^1(M, R), which measures the complexity of a dual surface, is an upper bound for the Alexander norm. He asked if these two norms were equal on all of H^1(M,R) when M fibers over the circle. Here, I give examples which show that the answer to this question is emphatically no. This question is related to the faithfulness of the Gassner representations of the braid groups. The key tool used to understand this question is the Bieri-Neumann-Strebel invariant from combinatorial group theory. Theorem 1.7, which is of independant interest, connects the Alexander polynomial with a certain Bieri-Neumann-Strebel invariant." @default.
- W2951237014 created "2019-06-27" @default.
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- W2951237014 date "1999-08-11" @default.
- W2951237014 modified "2023-09-28" @default.
- W2951237014 title "Alexander and Thurston norms of fibered 3-manifolds" @default.
- W2951237014 hasPublicationYear "1999" @default.
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