We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.

A surface in the 4-sphere is trivially embedded, if it bounds a 3dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the Rokhlin quadratic form of this embedded surface. AMS Classification 57N10; 57N05, 20F38

Suppose M is a tracial von Neumann algebra embeddable into R ω (the ultraproduct of the hyperfinite II 1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k, γ). We say that X is tubular if for any ǫ > 0 there exist m ∈ N

A new invariant, the Pontrjagin-Viro form, of algebraic surfaces is introduced and studied. It is related to various Rokhlin-Guillou-Marin forms and generalizes Mikhalkin’s complex separation. The form is calculated for all real Enriques surfaces for which it is well defined.

We extend the “miraculous cancellation” formulas of Alvarez– Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruences due to Ochanine, Finashin and Zhang. In particular, an analytic proof of the Finashin congruence is given.

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the CalderonZygmund kernel to obtain some fine estimates on the operator and prove the T(\) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et at., and Han and Hofmann. 2000 Mathematics subject classification: primary 42B20, 46B30.

We generalize the “miraculous cancellation” formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruence formulas of Ochanine [O1], Finashin [F] and Zhang [Z1, 2]. In particular, an analytic proof of the Finashin congruence formu...

We give an example of a simple separable C*-algebra which is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a unique tracial state. It has trivial K1, and its K0-group is order isomorphic to a countable subgroup of R.

In this note, we show that the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of any locally universal, McDuff II1 factor does not have quantifier elimination. We also show how a positive solution to the Connes Embedding Problem implies that there can be no modelcomplete theory of II1 factors.

The paper is devoted to the study of topologies on the group Aut(X, B) of all Borel automorphisms of a standard Borel space (X, B). Several topologies are introduced and all possible relations between them are found. One of these topologies, τ , is a direct analogue of the uniform topology widely used in ergodic theory. We consider the most natural subsets of Aut(X, B) and find their closures. ...