A norm for the cohomology of 2-complexes

Details A norm for the cohomology of 2-complexes A norm for the cohomology of 2-complexes

2002-03-05

arxiv.org/abs/math/0203042v1

Algebr. Geom. Topol. 2 (2002) 137-155

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-7.abs.html

Scientific paper

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 H^1(X; R) determined by graphs on X majorates the Alexander-Fox norms derived from \pi_1(X).

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