A function on the homology of 3–manifolds

Turaev, Vladimir

doi:10.2140/agt.2007.7.135

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A function on the homology of 3–manifolds

Vladimir Turaev

Algebraic & Geometric Topology 7 (2007) 135–156

DOI: 10.2140/agt.2007.7.135

arXiv: math.GT/0611149

Abstract

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

Keywords

genus, Thurston norm, torsion

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57Q10

References

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

Volume 7, issue 1 (2007)