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 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.

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