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We show that for each discrete group Γ, the rational assembly map
is injective on classes dual to , where Λ* is the subring generated by cohomology classes of degree at most 2 (and where the pairing uses the Chern character). Our
result implies homotopy invariance of higher signatures associated to classes in Λ*. This consequence was first established by Connes–Gromov–Moscovici (Geom. Funct. Anal. 3(1): 1–78, 1993) and Mathai (Geom.
Dedicata 99: 1–15, 2003). Note, however that the above injectivity statement does not follow from their methods. Our approach
is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our work
(Hanke and Schick, J. Differential Geom. 74: 293–320, 2006). In contrast to the argument in Connes-Gromov-Moscovici (Geom.
Funct.Anal. 3(1): 1–78, 1993), our approach is independent of (and indeed gives a new proof of) the result of Hilsum–Skandalis
(J. Reine Angew. Math. 423: 73–99, 1999) on the homotopy invariance of the index of the signature operator twisted with bundles
of small curvature.
相似文献
3.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献
4.
Kun-yu GUO & Peng-hui WANG School of Mathematics Pudan University Shanghai China 《中国科学A辑(英文版)》2007,(3)
In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. 相似文献
5.
Gong Guihua 《偏微分方程通讯》2013,38(1-2):341-362
In this paper, we discuss the following conjecture raised by Baum and Douglas: For any first order elliptic differential operator D on a smooth manifold M with boundary ?M D possesses a (local) elliptic boundary condition if and only if ?[D]=0 in K1(?M), where [D] is the relative K-cycle in Ko(M,?M) corresponding to D. We prove the “if” part of this conjecture for dim(M)≠4,5,6,7 and the “only if” part of the conjecture for arbitrary dimension. 相似文献
6.
Rechard Zekri 《K-Theory》1998,13(1):69-80
Given a C*-algebra A, and an ideal J of A, we define a relative group K^0(A,J) in terms of a relative universal C*-algebra for the pair (A,J). We show that the natural restriction map K^0(A,J) K0(J) is an isomorphism, and that, if J is a semisplit ideal of A, the Baum–Douglas–Taylor relative K-homology is recovered. This provides a generalization of one of the main results of the Baum–Douglas–Taylor theory. 相似文献
7.
In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. 相似文献
8.
Guoliang Yu 《K-Theory》1997,11(4):307-318
We introduce a localization algebra to define a local index mapo from K-homology to the K-theory of the localization algebra. we show that the local index map is an isomorphism. We apply this result to study the coarse Baum-Connes conjecture. 相似文献
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