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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Twisted Alexander norms give lower bounds on the Thurston norm


Authors: Stefan Friedl and Taehee Kim
Journal: Trans. Amer. Math. Soc. 360 (2008), 4597-4618
MSC (2000): Primary 57M27; Secondary 57N10
DOI: https://doi.org/10.1090/S0002-9947-08-04455-3
Published electronically: April 24, 2008
MathSciNet review: 2403698
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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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Additional Information

Stefan Friedl
Affiliation: Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec, Canada – and – Department of Mathematics, University of Warwick, Coventry, United Kingdom
Email: sfriedl@gmail.com

Taehee Kim
Affiliation: Department of Mathematics, Konkuk University, Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea
Email: tkim@konkuk.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-08-04455-3
Keywords: Thurston norm, twisted Alexander norm, 3-manifolds
Received by editor(s): June 1, 2005
Received by editor(s) in revised form: March 20, 2006
Published electronically: April 24, 2008
Additional Notes: The second author is the corresponding author for this paper
Article copyright: © Copyright 2008 American Mathematical Society