Thurston’s norm revisited
نویسنده
چکیده
We study Thurston’s norm on the second homology of a 3-manifold. The novelty of our approach consists in the use of methods of the C∗algebra theory. Namely, for Stallings’ fibration M with pseudo-Anosov monodromy, we associate a C∗-algebra whose K-theory gives rise to an algebraic number field K. We show that the trace function on the ring of integers of K induces a norm on the second homology of M . Further developments of this theory are discussed.
منابع مشابه
Thurston norm revisited
We study noncommutative C∗-algebras arising in geometric topology. Our object are Thurston’s norms on the second homology of Stallings’ fibrations. It is shown that Thurston’s norm is a matter of pure algebra, if one looks at the Bratteli diagram of an AF C∗-algebra attached to measured geodesic laminations on a compact surface of genus greater or equal to 2. This approach leads to computationa...
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