Algebraic and Geometric Topology 2 (2002),
paper no. 7, pages 137-155.
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 \pi_1(X).
Group cohomology, norms, 2-complexes, Alexander-Fox polynomials
AMS subject classification.
Submitted: 1 October 2001.
Accepted: 6 February 2002.
Published: 28 February 2002.
Notes on file formats
IRMA, Universite Louis Pasteur -- CNRS
7 rue Rene Descartes, 67084 Strasbourg, France
AGT home page
These pages are not updated anymore.
They reflect the state of
For the current production of this journal, please refer to