Algebraic & Geometric Topology

A function on the homology of 3–manifolds

Vladimir Turaev

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In analogy with the Thurston norm, we define for an orientable 3–manifold M a numerical function on H2(M;). This function measures the minimal complexity of folded surfaces representing a given homology class. A similar function is defined on the torsion subgroup of H1(M;). These functions are estimated from below in terms of abelian torsions of M.

Article information

Algebr. Geom. Topol., Volume 7, Number 1 (2007), 135-156.

Received: 21 November 2006
Accepted: 11 January 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]

genus Thurston norm torsion


Turaev, Vladimir. A function on the homology of 3–manifolds. Algebr. Geom. Topol. 7 (2007), no. 1, 135--156. doi:10.2140/agt.2007.7.135.

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