## Algebraic & Geometric Topology

### A function on the homology of 3–manifolds

#### Abstract

In analogy with the Thurston norm, we define for an orientable 3–manifold $M$ a numerical function on $H2(M;ℚ∕ℤ)$. This function measures the minimal complexity of folded surfaces representing a given homology class. A similar function is defined on the torsion subgroup of $H1(M;ℤ)$. These functions are estimated from below in terms of abelian torsions of $M$.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 1 (2007), 135-156.

Dates
Accepted: 11 January 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796662

Digital Object Identifier
doi:10.2140/agt.2007.7.135

Mathematical Reviews number (MathSciNet)
MR2308939

Zentralblatt MATH identifier
1145.57011

Keywords
genus Thurston norm torsion

#### Citation

Turaev, Vladimir. A function on the homology of 3–manifolds. Algebr. Geom. Topol. 7 (2007), no. 1, 135--156. doi:10.2140/agt.2007.7.135. https://projecteuclid.org/euclid.agt/1513796662

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