Geometry & Topology Volume 22, issue 6 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

$C^*$–algebraic higher signatures and an invariance theorem in codimension two

Nigel Higson, Thomas Schick and Zhizhang Xie

Geometry & Topology 22 (2018) 3671–3699

DOI: 10.2140/gt.2018.22.3671

Bibliography

1	O Attie, Quasi-isometry classification of some manifolds of bounded geometry, Math. Z. 216 (1994) 501 MR1288043
2	P Baum, A Connes, N Higson, Classifying space for proper actions and K–theory of group C^∗–algebras, from: "C^∗–algebras : 1943–1993" (editor R S Doran), Contemp. Math. 167, Amer. Math. Soc. (1994) 240 MR1292018
3	J Chabert, Baum–Connes conjecture for some semi-direct products, J. Reine Angew. Math. 521 (2000) 161 MR1752299
4	G Gong, Q Wang, G Yu, Geometrization of the strong Novikov conjecture for residually finite groups, J. Reine Angew. Math. 621 (2008) 159 MR2431253
5	M Gromov, H B Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983) 83 MR720933
6	E Guentner, N Higson, S Weinberger, The Novikov conjecture for linear groups, Publ. Math. Inst. Hautes Études Sci. 101 (2005) 243 MR2217050
7	B Hanke, D Pape, T Schick, Codimension two index obstructions to positive scalar curvature, Ann. Inst. Fourier (Grenoble) 65 (2015) 2681 MR3449594
8	N Higson, A note on the cobordism invariance of the index, Topology 30 (1991) 439 MR1113688
9	N Higson, J Roe, Mapping surgery to analysis, I : Analytic signatures, K–Theory 33 (2005) 277 MR2220522
10	N Higson, J Roe, Mapping surgery to analysis, II : Geometric signatures, K–Theory 33 (2005) 301 MR2220523
11	N Higson, J Roe, Mapping surgery to analysis, III : Exact sequences, K–Theory 33 (2005) 325 MR2220524
12	N Higson, J Roe, G Yu, A coarse Mayer–Vietoris principle, Math. Proc. Cambridge Philos. Soc. 114 (1993) 85 MR1219916
13	M Hilsum, G Skandalis, Invariance par homotopie de la signature à coefficients dans un fibré presque plat, J. Reine Angew. Math. 423 (1992) 73 MR1142484
14	G G Kasparov, Equivariant K“K–theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
15	G G Kasparov, K–theory, group C^∗–algebras, and higher signatures (conspectus), from: "Novikov conjectures, index theorems and rigidity, I" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 101 MR1388299
16	M Land, T Nikolaus, On the relation between K– and L–theory of C^∗–algebras, Math. Ann. 371 (2018) 517 MR3788857
17	A S Miščenko, Infinite-dimensional representations of discrete groups, and higher signatures, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974) 81 MR0362407
18	S P Novikov, Algebraic construction and properties of Hermitian analogs of K–theory over rings with involution from the viewpoint of Hamiltonian formalism : applications to differential topology and the theory of characteristic classes, I, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 253 MR0292913
19	S P Novikov, Algebraic construction and properties of Hermitian analogs of K–theory over rings with involution from the viewpoint of Hamiltonian formalism : applications to differential topology and the theory of characteristic classes, II, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 475 MR0292913
20	P Piazza, T Schick, The surgery exact sequence, K–theory and the signature operator, Ann. K–Theory 1 (2016) 109 MR3514938
21	J Roe, Partitioning noncompact manifolds and the dual Toeplitz problem, from: "Operator algebras and applications, I" (editors D E Evans, M Takesaki), London Math. Soc. Lecture Note Ser. 135, Cambridge Univ. Press (1988) 187 MR996446
22	J Roe, Coarse cohomology and index theory on complete Riemannian manifolds, 497, Amer. Math. Soc. (1993) MR1147350
23	J Roe, Index theory, coarse geometry, and topology of manifolds, 90, Amer. Math. Soc. (1996) MR1399087
24	J Rosenberg, Analytic Novikov for topologists, from: "Novikov conjectures, index theorems and rigidity, I" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 338 MR1388305
25	J Rosenberg, Novikov’s conjecture, from: "Open problems in mathematics" (editors J F Nash Jr., M T Rassias), Springer (2016) 377 MR3526942
26	T Schick, M E Zadeh, Large scale index of multi-partitioned manifolds, J. Noncommut. Geom. 12 (2018) 439 MR3825192
27	C Wahl, Higher ρ–invariants and the surgery structure set, J. Topol. 6 (2013) 154 MR3029424
28	C T C Wall, Surgery on compact manifolds, 69, Amer. Math. Soc. (1999) MR1687388
29	G Yu, The Novikov conjecture for groups with finite asymptotic dimension, Ann. of Math. 147 (1998) 325 MR1626745
30	M E Zadeh, Index theory and partitioning by enlargeable hypersurfaces, J. Noncommut. Geom. 4 (2010) 459 MR2670972