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A norm for the cohomology of 2–complexes

Vladimir Turaev

Algebraic & Geometric Topology 2 (2002) 137–155

arXiv: math.AT/0203042

Abstract

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; ) determined by graphs on X majorates the Alexander–Fox norms derived from π1(X).

Keywords
group cohomology, norms, 2–complexes, Alexander–Fox polynomials
Mathematical Subject Classification 2000
Primary: 57M20
Secondary: 57M05
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Publication
Received: 1 October 2001
Accepted: 6 February 2002
Published: 28 February 2002
Authors
Vladimir Turaev
IRMA, Université Louis Pasteur
CNRS
7 rue René Descartes
67084 Strasbourg
France