The Coarse p-Novikov Conjecture and Banach Spaces with Property (H)

Huan Wang , Qin Wang

Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (2) : 193 -220.

PDF
Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (2) : 193 -220. DOI: 10.1007/s11401-024-0012-x
Article

The Coarse p-Novikov Conjecture and Banach Spaces with Property (H)

Author information +
History +
PDF

Abstract

In this paper, for 1 < p < ∞, the authors show that the coarse p-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property (H).

Keywords

The coarse p-Novikov conjecture / Banach spaces with Property (H) / Coarse geometry / K-Theory

Cite this article

Download citation ▾
Huan Wang, Qin Wang. The Coarse p-Novikov Conjecture and Banach Spaces with Property (H). Chinese Annals of Mathematics, Series B, 2024, 45(2): 193-220 DOI:10.1007/s11401-024-0012-x

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Chen X, Wang Q, Yu G. The coarse Novikov conjecture and Banach spaces with Property (H). J. Funct. Anal., 2015, 268(9): 2754-2786

[2]

Chung Y C, Li K. Rigidity of p Roe-type algebras. Bull. Lond. Math. Soc., 2018, 50(6): 1056-1070

[3]

Chung, Y. C. and Nowak, P. W., Expanders are counterexamples to the coarse p-Baum-Connes conjecture, 2018, arXiv: 1811.10457.

[4]

Higson N, Roe J. On the Coarse Baum-Connes Conjecture, Novikov Conjectures, Index Theorems and Rigidity, 2 (Oberwolfach, 1993), 1995, Cambridge: Cambridge Univ. Press 227-254

[5]

Kasparov G G. Equivariant KK-theory and the Novikov conjecture. Invent. Math., 1988, 91(1): 147-201

[6]

Kasparov G G, Yu G. The coarse geometric Novikov conjecture and uniform convexity. Adv. Math., 2006, 206(1): 1-56

[7]

Kasparov G G, Yu G. The Novikov conjecture and geometry of Banach spaces. Geom. Topol., 2012, 16(3): 1859-1880

[8]

Lafforgue V. K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes. Invent. Math., 2002, 149(1): 1-95

[9]

Lafforgue V. K-théorie bivariante pour les algèbres de Banach, groupoïdes et conjecture de Baum-Connes, Avec un appendice d’Hervé Oyono-Oyono.. J. Inst. Math. Jussieu., 2007, 6(3): 415-451

[10]

Liao, B. and Yu, G., K-theory of group Banach algebras and Banach property RD, 2017, arXiv: 1708.01982.

[11]

Qiao Y, Roe J. On the localization algebra of Guoliang Yu. Forum Math., 2010, 22(4): 657-665

[12]

Roe, J., Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc., 104 (497) 1993, x+90 pp.

[13]

Shan L, Wang Q. The coarse geometric Novikov conjecture for subspaces of non-positively curved manifolds. J. Funct. Anal., 2007, 248(2): 448-471

[14]

Shan L, Wang Q. The Coarse Geometric p-Novikov Conjecture for Subspaces of Non-positively Curved Manifolds. J. Noncommut. Geom., 2021, 15(4): 1323-1354

[15]

Yu G. Coarse Baum-Connes conjecture. K-theory, 1995, 9(3): 199-221

[16]

Yu G. Baum-Connes conjecture and coarse geometry. K-theory, 1995, 9(3): 223-231

[17]

Yu G. Localization algebras and the coarse Baum-Connes conjecture. K-theory, 1997, 11(4): 307-318

[18]

Yu G. The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space. Invent. Math., 2000, 139(1): 201-240

[19]

Yu G. Hyperbolic groups admit proper affine isometric actions on p-spaces. Geom. Funct. Anal., 2005, 15(5): 1144-1151

[20]

Zhang J, Zhou D. p Coarse Baum-Connes conjecture and K-theory for L p Roe algebras. J. Noncommut. Geom., 2021, 15(4): 1285-1322

AI Summary AI Mindmap
PDF

200

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/