#### Volume 7, issue 1 (2007)

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A function on the homology of 3–manifolds

### Vladimir Turaev

Algebraic & Geometric Topology 7 (2007) 135–156
 arXiv: math.GT/0611149
##### Abstract

In analogy with the Thurston norm, we define for an orientable 3–manifold $M$ a numerical function on ${H}_{2}\left(M;ℚ∕ℤ\right)$. This function measures the minimal complexity of folded surfaces representing a given homology class. A similar function is defined on the torsion subgroup of ${H}_{1}\left(M;ℤ\right)$. These functions are estimated from below in terms of abelian torsions of $M$.

##### Keywords
genus, Thurston norm, torsion
Primary: 57M27
Secondary: 57Q10
##### Publication
Received: 21 November 2006
Accepted: 11 January 2007
Published: 29 March 2007
##### Authors
 Vladimir Turaev IRMA, CNRS et Université Louis Pasteur 7 rue René Descartes 67084 Strasbourg France Department of Mathematics Indiana University Bloomington IN 47405 USA