The Novikov conjecture and geometry of Banach spaces

Kasparov, Gennadi¹ ; Yu, Guoliang²

¹ Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240, USA
² Department of Mathematics, Texas A&M University, College Station TX 77843, USA, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China

Geometry & topology, Tome 16 (2012) no. 3, pp. 1859-1880.

Résumé

In this paper, we prove the strong Novikov conjecture for groups coarsely embeddable into Banach spaces satisfying a geometric condition called Property (H).

Détail

DOI : 10.2140/gt.2012.16.1859

Classification : 19K35, 19K56, 46L80, 57R55
Keywords: Novikov conjecture, Banach space

Bibliographie

[1] M F Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. 19 (1968) 113

[2] P Baum, A Connes, N Higson, Classifying space for proper actions and $K$–theory of group $C^{*}$–algebras, from: "$C^{*}$–algebras: 1943–1993 (San Antonio, TX, 1993)", Contemp. Math. 167, Amer. Math. Soc. (1994) 240

[3] Y Benyamini, J Lindenstrauss, Geometric nonlinear functional analysis Vol. 1, American Mathematical Society Colloquium Publications 48, American Mathematical Society (2000)

[4] N Brown, E Guentner, Uniform embeddings of bounded geometry spaces into reflexive Banach space, Proc. Amer. Math. Soc. 133 (2005) 2045

[5] M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2 (Sussex, 1991)", London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1

[6] E Guentner, N Higson, J Trout, Equivariant $E$–theory for $C^{*}$–algebras, Mem. Amer. Math. Soc. 148 (2000)

[7] N Higson, Bivariant $K$–theory and the Novikov conjecture, Geom. Funct. Anal. 10 (2000) 563

[8] N Higson, G Kasparov, J Trout, A Bott periodicity theorem for infinite-dimensional Euclidean space, Adv. Math. 135 (1998) 1

[9] W B Johnson, N L Randrianarivony, $l_p (p\gt 2)$ does not coarsely embed into a Hilbert space, Proc. Amer. Math. Soc. 134 (2006) 1045

[10] G Kasparov, G Skandalis, Groups acting properly on “bolic” spaces and the Novikov conjecture, Ann. of Math. 158 (2003) 165

[11] M Mendel, A Naor, Metric cotype, Ann. of Math. 168 (2008) 247

[12] J Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 104 (1993)

[13] G Skandalis, J L Tu, G Yu, The coarse Baum–Connes conjecture and groupoids, Topology 41 (2002) 807

[14] G Yu, Localization algebras and the coarse Baum–Connes conjecture, $K$–Theory 11 (1997) 307

[15] G Yu, The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139 (2000) 201