TheK-theory of AF embeddings of the rational rotation algebras

Our main result is the construction of an embedding ofC(T²) into an approximately finite-dimensionalC ^*-algebra which induces an injection onK ₀(C(T²)). The existence of this embedding implies that Cech cohomology cannot be extended to a stable, continuous homology theory forC ^*-algebras which admits a well-behaved Chern character. Homotopy properties ofC ^*-algebras are also considered. For example, we show that the second homotopy functor forC ^*-algebras is discontinuous. Similar embeddings are constructed for all the rational rotation algebras, with the consequence that none of the rational rotation algebras satisfies the homotopy property called semiprojectivity.     

范畴 RMRl上的一个函子及范畴A Grn0

本文定义了一个由范畴 _RM_R^l到范畴Ａ G_rn⁰ 的函子Ｇ，并证明了函子Ｇ保持分量正合及全正合，关于范畴ＡＧG_rn⁰ 证明了定理：     

Formality theorem for Lie bialgebras and quantization of twists and coboundary r-matrices

Let (g,δ?) be a Lie bialgebra. Let (U?(g),Δ?) a quantization of (g,δ?) through Etingof-Kazhdan functor. We prove the existence of a L_∞-morphism between the Lie algebra C(g)=Λ(g) and the tensor algebra (without unit) T₊U=T₊(U?(g)[−1]) with Lie algebra structure given by the Gerstenhaber bracket. When s is a twist for (g,δ), we deduce from the formality morphism the existence of a quantum twist F. When (g,δ,r) is a coboundary Lie bialgebra, we get the existence of a quantization R of r.     

Homotopy of the classical configuration space for the two-magnon sector of a magnetic Heisenberg ring

A finite Heisenberg magnetic ring with an arbitrary single-node spin and two spin deviations from the ferromagnetic saturation is considered as the system of two Bethe pseudoparticles. The set of all relevant magnetic configurations spans a surface which can be recognised as a Mőbius strip. The dynamics of the system imposes the double twist of all regular orbits of the translation symmetry group.     

C^＊-代数中的等价

在算子理论和算子代数的研究中，等价是一个很重要的工具，它对K-理论的研究和理解起着很重要的作用．寻找等价关系是研究不变量的一种方法，为了使大家更好的认识和学习C^＊-代数，我们在本文研究了算子代数中经常用到的代数等价、酉等价、同伦等几种等价之间的关系．     

A Z/2 Descent Theorem for the Algebraic K-Theory of a Semisimple Real Algebra

On algebraic K-theory of a finite-dimensional semisimple real algebra the involution induced by an antistructure is studied. After Bousfield–Kan completion at 2, a component of the homotopy fixed point set is homotopy-equivalent to the fixed point set. The fixed point set is calculated.     

Topological,affine and isometric actions on flat riemannian manifolds II

Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π₀(Homeo(M))→Out π₁(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau.     

函子的广义逆

本文建立了函子的广义逆．得到：（１）函子的广义逆从不同于视矩阵为态射的另一角度，包含了“矩阵的广义逆”．（２）函子的广义道与态射的广义逆互不蕴含，但却有异曲同工之处．     

Embedding up to homotopy type— The first obstruction

For a 2n?m connected map from an n-dimensional complex to a m-dimensional manifold, an obstruction to embedding up to homotopy type is defined. The vanishing of this obstruction is a necessary and sufficient condition (in the 2n?m connected case, 2n?m ? 2, m?n ?3) to obtain an embedding up to homotopy type. In case the target manifold is Euclidean space, it is shown that the obstruction vanishes if and only if certain Thom operations are trivial. A classification theorem is given in the 2n?m+1 connected case.     

A note on asymptotic homomorphisms

Using the notion of asymptotic homomorphism due to Connes and Higson we construct bivariant homology-cohomology theories for separableC*-algebras, which satisfy general excision axioms and are nonperiodic.