Osaka Journal of Mathematics

The virtual Thurston seminorm of 3-manifolds

Michel Boileau and Stefan Friedl

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We show that the Thurston seminorms of all finite covers of an aspherical 3-manifold determine whether it is a graph manifold, a mixed 3-manifold or hyperbolic.

Article information

Osaka J. Math., Volume 56, Number 1 (2019), 51-63.

First available in Project Euclid: 16 January 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M05: Fundamental group, presentations, free differential calculus 57M10: Covering spaces 57M27: Invariants of knots and 3-manifolds


Boileau, Michel; Friedl, Stefan. The virtual Thurston seminorm of 3-manifolds. Osaka J. Math. 56 (2019), no. 1, 51--63.

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