In analogy with the Thurston norm, we define for an orientable 3–manifold a numerical function on . This function measures the minimal complexity of folded surfaces representing a given homology class. A similar function is defined on the torsion subgroup of . These functions are estimated from below in terms of abelian torsions of .
"A function on the homology of 3–manifolds." Algebr. Geom. Topol. 7 (1) 135 - 156, 2007. https://doi.org/10.2140/agt.2007.7.135