A function on the homology of 3-manifolds

Details A function on the homology of 3-manifolds A function on the homology of 3-manifolds

2006-11-06

arxiv.org/abs/math/0611149v2

Mathematics

Geometric Topology

16 pages, no figures. The second version incorporates several minor corrections

Scientific paper

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 $H_1(M)$. These functions are
estimated from below in terms of abelian torsions of $M$.

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