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- W3101415511 abstract "The conjugacy problem for the pseudo-Anosov automorphisms of a compact surface is studied. To each pseudo-Anosov automorphism f, we assign an AF-algebra A(f) (an operator algebra). It is proved that the assignment is functorial, i.e. every f', conjugate to f, maps to an AF-algebra A(f'), which is stably isomorphic to A(f). The new invariants of the conjugacy of the pseudo-Anosov automorphisms are obtained from the known invariants of the stable isomorphisms of the AF-algebras. Namely, the main invariant is a triple (L, [I], K), where L is an order in the ring of integers in a real algebraic number field K and [I] an equivalence class of the ideals in L. The numerical invariants include the determinant D and the signature S, which we compute for the case of the Anosov automorphisms. A question concerning the p-adic invariants of the pseudo-Anosov automorphism is formulated." @default.
- W3101415511 created "2020-11-23" @default.
- W3101415511 creator A5030662408 @default.
- W3101415511 date "2013-03-20" @default.
- W3101415511 modified "2023-10-18" @default.
- W3101415511 title "Operator algebras and conjugacy problem for the pseudo-Anosov automorphisms of a surface" @default.
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- W3101415511 doi "https://doi.org/10.2140/pjm.2013.261.445" @default.
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