Thurston's norm revisited

Details Thurston's norm revisited Thurston's norm revisited

2002-06-19

arxiv.org/abs/math/0206201v4

Far East J. Math. Sci. (FJMS) 41 (2010), 1-12

Mathematics

Geometric Topology

9 pages, to appear Far East J. Math. Sciences

Scientific paper

We study the Thurston norm on the second homology of a 3-manifold M, which is the surface bundle over the circle with a pseudo-Anosov monodromy. A novelty of our approach consists in the application of the C*-algebras to a problem in topology. Namely, one associates to M a C*-algebra, whose K-theory gives rise to an algebraic number field K. It is shown, that the trace function on the ring of integers of K induces a norm on the second homology of M. The norm coincides with the Thurston norm on the second homology of M.

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