Geodesic
A function on the homology of 3–manifolds
Turaev, Vladimir1
1IRMA, CNRS et Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France, Department of Mathematics, Indiana University, Bloomington IN 47405, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 135-156
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In analogy with the Thurston norm, we define for an orientable 3–manifold M a numerical function on H2(M; ℚ∕ℤ). 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; ℤ). These functions are estimated from below in terms of abelian torsions of M.

DOI : 10.2140/agt.2007.7.135
Keywords: genus, Thurston norm, torsion

Turaev, Vladimir  1

1 IRMA, CNRS et Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France, Department of Mathematics, Indiana University, Bloomington IN 47405, USA 
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Turaev, Vladimir. A function on the homology of 3–manifolds. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 135-156. doi: 10.2140/agt.2007.7.135

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