SS1 - Algèbres d'opérateurs / SS1 - Operator algebras
Org: C. Anantharaman (Orléans) et/and I. Putnam (Victoria)
- MOULAY BENAMEUR, Université de Metz
The index theorem in Haefliger cohomology
We shall first define the Gysin maps in Haefliger cohomology and show
their compatibility with the Gysin maps in K-theory. This yields an
easy computation of the topological longitudinal index map. When the
Novikov-Shubin invariants of the foliation are greater than half the
codimension, we prove that the Chern character of the analytical
longitudinal index coincides with the index bundle. This improves a
previous result of Heitsch and Lazarov.
Joint work with J. Heitsch.
- JEROME CHABERT, Université Blaise Pascal, Clermont-Ferrand
Kuenneth formula and the Baum-Connes conjecture
In this joint work with Siegfried Echterhoff and Hervé Oyono-Oyono, we
formalize a method for proving results on the topological K-theory
of a group G-the left-hand side of the Baum-Connes conjecture for
G-by reducing to certain compact subgroups of G. Using this
method, we obtain that this conjecture is stable under various
operations on the group G, and we investiguate the connections
between the Kuenneth formula for the C*-algebra of G and the
change of coefficient algebra in the Baum-Connes conjecture.
In particular, we show that the adelic group corresponding to a linear
algebraic group over a finite extension of Q satisfies the
conjecture for coefficient algebras with no action.
- GEORGE ELLIOTT, University of Toronto, Toronto, Canada
Recent results concerning the classification of (separable) amenable
C*-algebras will be surveyed. A fairly clearly defined dichotomy
is appearing between a class of especially well-behaved amenable
C*-algebras, and the rest (typified by examples of Villadsen, and
later also of Rordam and Toms).
- HEATH EMERSON, University of Victoria, Canada
Asymptotic geometry of groups and the Novikov conjecture
We introduce the notion of an `asymptotic K-theory class' for a
group G. Such classes, which are cohomology classes for BG, may
be regarded as arising from dyanamics, or from large-scale
geometry. Every asymptotic K-theory class satisfies the Novikov
conjecture, i.e. is homotopy-invariant. The set of asymptotic
K-classes may be gathered into a single geometric K-theory group
which maps to the ordinary K-theory of BG. We give some examples
and show how our framework allows one to prove that existence of a
g-element for a group G is a quasi-isometry invariant of the
- DAMIEN GABORIAU, ENS-Lyon, UMPA-UMR CNRS 5669, 46 allée d'Italie, 69364 Lyon
Some invariants for equivalence relations and factors
Type II1 equivalence relations R are produced for
instance by probability measure preserving actions of countable groups
or by holonomy pseudogroups of measured laminations. To such an
R is associated its sequence of L2-Betti
numbers. They are associated with pairs of von Neumann algebra/Cartan
subalgebras. These numbers are just multiplied by a constant when one
restricts R to a big enough Borel subset. This property
enables S. Popa to produce the first example of a factor with a
trivial fundamental group. I'll try to give some ideas about the
- THIERRY GIORDANO, Université d'Ottawa, Ottawa
Orbit equivalence of minimal actions on the Cantor set
Both in the measurable and in the Borel case, hyperfinite actions are
well understood and classified up to orbit equivalence. In particular
any free Borel action of Z2 is (orbit equivalent to) hyperfinite.
In the case of (minimal) topological actions of Z2 on the Cantor
set, the same question is still open. In this talk, I will present
recent developments in the study of this problem. These developments
come from a work in progress with I. Putnam (University of Victoria)
and C. Skau (NTNU, Trondheim).
- DAVID KERR, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
C*-dynamics and contractive approximation entropy
We develop a Banach space analogue of Voiculescu-Brown entropy and
discuss its advantages and limitations as an invariant for
C*-dynamical systems. This is joint work with Hanfeng Li.
- MARCELO LACA, University of Victoria
Boundary quotients of Toeplitz algebras of Artin groups
I will talk about the Toeplitz C*-algebras of Artin groups of
rectangular type, and the simple quotients that arise from
considering a certain partial action on the boundary determined by the
corresponding Artin monoid.
Joint work with J. Crisp.
- SEVERINO T. MELO, Universidade de Sao Paulo, Caixa Postal 66281, 05311-970, Sao
A K-theoretic proof of Boutet de Monvel's index theorem
Let A denote the C*-closure of the algebra of all polyhomogeneous
operators of order and class zero in Boutet de Monvel's calculus on a
connected compact manifold X with nonempty boundary. We derive a
natural short exact sequence
which splits in a not necessarily natural way. Here K is the
compact ideal and TX¢ is the cotangent bundle of the interior
0® Ki ||
® Ki (A/K) ® K1-i (TX¢) ® 0,|
We also give a K-theoretic proof of the fact that the composition of
the topological index with the mapping from K1 (A/K) to K0 (TX¢)
in the above sequence gives the Fredholm-index homomorphism. That the
Fredholm index for A factors through K(TX¢) was first proven by
Boutet de Monvel.
This is joint work with Thomas Schick and Elmar Schrohe, based on
previous joint work with Ryszard Nest and Elmar Schrohe.
- JEAN RENAULT, Université d'Orléans, BP 6759, 45067 Orléans Cedex 2
Mesures de Gibbs sur les relations d'équivalence AP
Il s'agit de déterminer l'ensemble, ou au moins d'étudier
l'existence et l'unicité, des mesures quasi-invariantes sur une
relation d'équivalence admettant un cocycle donné comme
dérivée de Radon-Nikodym. Quand la relation d'équivalence est
approximativement propre, c'est-à-dire réunion d'une suite
croissante de relations d'équivalence propres, on peut utiliser la
caractérisation de Dobrushin, Lanford et Ruelle des mesures de Gibbs
et des résultats de Goodearl sur les groupes de dimension pour
établir dans certains cas l'unicité. Nous présenterons aussi une
version C*-algébrique de ces résultats, dont certains ont
été obtenus en collaboration avec R. Exel et A. Kumjian.