AF-algebras and topology of 3-manifolds

Details AF-algebras and topology of 3-manifolds AF-algebras and topology of 3-manifolds

2001-10-20

arxiv.org/abs/math/0110227v7

Mathematics

Geometric Topology

15 pages, 1 figure

Scientific paper

We construct a functor which maps conjugate pseudo-Anosov automorphisms of a surface to the so-called stably isomorphic stationary AF-algebras; the functor gives new topological invariants of three dimensional manifolds coming from the known invariants of the AF-algebras. The main invariant is a triple (L, [I], K), where L is an integral order in the real number field K and [I] the equivalence class of ideals in L.

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