Geodesic
A norm for the cohomology of 2–complexes
Turaev, Vladimir1
1IRMA, Université Louis Pasteur, CNRS, 7 rue René Descartes, 67084 Strasbourg, France
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 137-155
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We introduce a norm on the real 1–cohomology of finite 2–complexes determined by the Euler characteristics of graphs on these complexes. We also introduce twisted Alexander–Fox polynomials of groups and show that they give rise to norms on the real 1–cohomology of groups. Our main theorem states that for a finite 2–complex X, the norm on H1(X; ℝ) determined by graphs on X majorates the Alexander–Fox norms derived from π1(X).

DOI : 10.2140/agt.2002.2.137
Keywords: group cohomology, norms, 2–complexes, Alexander–Fox polynomials

Turaev, Vladimir  1

1 IRMA, Université Louis Pasteur, CNRS, 7 rue René Descartes, 67084 Strasbourg, France 
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Turaev, Vladimir. A norm for the cohomology of 2–complexes. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 137-155. doi: 10.2140/agt.2002.2.137

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