A norm for the cohomology of 2–complexes

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 $π_{1} (X)$ .

Keywords

group cohomology, norms, 2–complexes, Alexander–Fox polynomials

Mathematical Subject Classification 2000

Primary: 57M20

Secondary: 57M05

References

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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

Volume 2, issue 1 (2002)

Vladimir Turaev