A function on the homology of 3-manifolds

Vladimir Turaev

doi:10.2140/agt.2007.7.135

A function on the homology of 3-manifolds

Geometric Topology 2014-10-01 v2

Authors: Vladimir Turaev

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

Keywords

orientable 3-manifold thurston norm folded surfaces homology class torsion subgroup abelian torsion

Cite

@article{arxiv.math/0611149,
  title  = {A function on the homology of 3-manifolds},
  author = {Vladimir Turaev},
  journal= {arXiv preprint arXiv:math/0611149},
  year   = {2014}
}

Comments

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

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