6 K - theory of hyperbolic 3 - manifolds
نویسنده
چکیده
We introduce an invariant of the hyperbolic 3-manifolds which appears in the K-theory of certain C*-algebras. Namely, such an invariant is essentially an algebraic number field K with a fixed equivalence class of ideals in the ring of integers of K. The C*-algebras in question are the crossed product C*-algebras attached to the monodromy transformation of the 3-manifolds which fiber over the circle. Our approach bridges topology with the number field theory. In particular, we conjecture a volume formula for the 3-manifolds in terms of the arithmetic of the field K.
منابع مشابه
6 M ay 2 00 6 K - invariants of hyperbolic 3 - manifolds
We introduce an invariant of the hyperbolic 3-manifolds which appears in the K-theory of certain C*-algebras. Namely, such an invariant is essentially the integral order in an algebraic number field K with a fixed equivalence class of ideals in the ring of integers of K. The C*-algebras in question are the crossed product C*-algebras attached to the monodromy transformation of the 3-manifolds w...
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