Igor Nikolaev
Notes on noncommutative algebraic topology.
Втр, 09/07/2010 - 15:01 — SomNambulAuthors: Igor Nikolaev
Subjects: Operator Algebras
AbstractAn operator (AF-) algebra A_f is assigned to each Anosov diffeomorphism f of
a manifold M. The assignment is a functor on the category of (mapping tori of)
all such diffeomorphisms, which sends continuous maps between the manifolds to
the stable homomorphisms of the corresponding AF-algebras. We use the functor
to prove non-existence of continuous maps between the hyperbolic torus bundles,
an obstruction being the so-called Galois group of algebra A_f.On a noncommutative reciprocity law.
Пт, 12/25/2009 - 16:01 — SomNambulAuthors: Igor Nikolaev
Subjects: Operator Algebras
AbstractA reciprocity conjecture for the noncommutative tori is proved. The
conjecture says that an L-function of the noncommutative torus with real
multiplication coincides with the Hasse-Weil L-function of an elliptic curve
with the complex multiplication. Our proof is based on an explicit formula for
the Teichmueller functor between the elliptic curves and noncommutative tori.On a zeta function of the noncommutative torus.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: Igor Nikolaev
Subjects: Number Theory
AbstractIt is shown how to extend the Selberg zeta function from the discontinuous
groups to the noncommutative tori. The extension gives a zeta function defined
on the noncommutative torus with real multiplication. An application of the
function to the period-rank conjecture is given.On a zeta function of the noncommutative torus.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: Igor Nikolaev
Subjects: Number Theory
AbstractIt is shown how to extend the Selberg zeta function from the discontinuous
groups to the noncommutative tori. The extension gives a zeta function defined
on the noncommutative torus with real multiplication. An application of the
function to the period-rank conjecture is given.Noncommutative localization.
Пт, 09/11/2009 - 19:12 — SomNambulAuthors: Igor Nikolaev
Subjects: Operator Algebras
AbstractThe Teichmueller functor maps the category of elliptic curves over the field
of characteristic zero to a category of the Effros-Shen algebras. In the
present note, we extend the functor to include the elliptic curves over the
field of characteristic p. In particular, it is shown that the localization of
a commutative ring at the maximal ideal corresponds to a crossed product of the
Effros-Shen algebra by the p-th power of its shift automorphism. The
Cuntz-Krieger algebra is, therefore, an example of the noncommutative local
ring.
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