Volume 10, issue 4 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
The general notion of descent in coarse geometry

Paul D Mitchener

Algebraic & Geometric Topology 10 (2010) 2419–2450
Bibliography
1 D R Anderson, F X Connolly, S C Ferry, E K Pedersen, Algebraic $K$–theory with continuous control at infinity, J. Pure Appl. Algebra 94 (1994) 25 MR1277522
2 A C Bartels, Squeezing and higher algebraic $K$–theory, $K$–Theory 28 (2003) 19 MR1988817
3 A C Bartels, F T Farrell, L E Jones, H Reich, On the isomorphism conjecture in algebraic $K$–theory, Topology 43 (2004) 157 MR2030590
4 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)" (editor R S Doran), Contemp. Math. 167, Amer. Math. Soc. (1994) 240 MR1292018
5 M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic $K$–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
6 G Carlsson, E K Pedersen, Controlled algebra and the Novikov conjectures for $K$– and $L$–theory, Topology 34 (1995) 731 MR1341817
7 J F Davis, W Lück, Spaces over a category and assembly maps in isomorphism conjectures in $K$– and $L$–theory, $K$–Theory 15 (1998) 201 MR1659969
8 A N Dranishnikov, Asymptotic topology, Uspekhi Mat. Nauk 55 (2000) 71 MR1840358
9 F T Farrell, L E Jones, Isomorphism conjectures in algebraic $K$–theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537
10 P Ghez, R Lima, J E Roberts, $W^{*}$–categories, Pacific J. Math. 120 (1985) 79 MR808930
11 E Guentner, R Tessera, G Yu, A notion of geometric complexity and its application to topological rigidity arXiv:1008.0884v1
12 I Hambleton, E K Pedersen, Identifying assembly maps in $K$– and $L$–theory, Math. Ann. 328 (2004) 27 MR2030369
13 N Higson, E K Pedersen, J Roe, $C^{*}$–algebras and controlled topology, $K$–Theory 11 (1997) 209 MR1451755
14 N Higson, J Roe, On the coarse Baum–Connes conjecture, from: "Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993)" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 227, Cambridge Univ. Press (1995) 227 MR1388312
15 N Higson, J Roe, Analytic $K$–homology, Oxford Math. Monogr., Oxford Sci. Publ., Oxford Univ. Press (2000) MR1817560
16 N Higson, J Roe, G L Yu, A coarse Mayer–Vietoris principle, Math. Proc. Cambridge Philos. Soc. 114 (1993) 85 MR1219916
17 M Joachim, $K$–homology of $C^{*}$–categories and symmetric spectra representing $K$–homology, Math. Ann. 327 (2003) 641 MR2023312
18 G G Kasparov, Equivariant $KK$–theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
19 G G Kasparov, $K$–theory, group $C^{*}$–algebras, and higher signatures (conspectus), from: "Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993)" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 101 MR1388299
20 M Kreck, W Lück, The Novikov conjecture. Geometry and algebra, Oberwolfach Seminars 33, Birkhäuser Verlag (2005) MR2117411
21 J L Loday, $K$–théorie algébrique et représentations de groupes, Ann. Sci. École Norm. Sup. $(4)$ 9 (1976) 309 MR0447373
22 V T Luu, Coarse categories i: Foundations arXiv:0708.3901
23 T Matumoto, Equivariant cohomology theories on $G$–$\mathrm{CW}$– complexes, Osaka J. Math. 10 (1973) 51 MR0343259
24 R McCarthy, On fundamental theorems of algebraic $K$–theory, Topology 32 (1993) 325 MR1217072
25 B Mitchell, Separable algebroids, Mem. Amer. Math. Soc. 57 (1985) MR804210
26 P D Mitchener, Algebraic $K$–theory spectra and factorisations of analytic assembly maps arXiv:0711.2182
27 P D Mitchener, Coarse homology theories, Algebr. Geom. Topol. 1 (2001) 271 MR1834777
28 P D Mitchener, Symmetric $K$–theory spectra of $C^{*}$–categories, $K$–Theory 24 (2001) 157 MR1869627
29 P D Mitchener, $C^{*}$–categories, Proc. London Math. Soc. $(3)$ 84 (2002) 375 MR1881396
30 P D Mitchener, Addendum to: “Coarse homology theories” \rm[Algebr. Geom. Topol. 1 (2001), 271–297; MR1834777], Algebr. Geom. Topol. 3 (2003) 1089 MR2012966
31 P D Mitchener, $C^{*}$–categories, groupoid actions, equivariant $KK$–theory, and the Baum–Connes conjecture, J. Funct. Anal. 214 (2004) 1 MR2079884
32 P D Mitchener, B Norouzizadeh, T Schick, Coarse homotopy theory, in preparation
33 E K Pedersen, C A Weibel, A nonconnective delooping of algebraic $K$–theory, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 166 MR802790
34 J Roe, Index theory, coarse geometry, and topology of manifolds, CBMS Regional Conference Ser. in Math. 90, Conference Board of Math. Sci. (1996) MR1399087
35 J Roe, Comparing analytic assembly maps, Q. J. Math. 53 (2002) 241 MR1909514
36 J Roe, Lectures on coarse geometry, Univ. Lecture Series 31, Amer. Math. Soc. (2003) MR2007488
37 F Waldhausen, Algebraic $K$–theory of spaces, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
38 M Weiss, Excision and restriction in controlled $K$–theory, Forum Math. 14 (2002) 85 MR1880196
39 M Weiss, B Williams, Assembly, from: "Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993)" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 227, Cambridge Univ. Press (1995) 332 MR1388318
40 N Wright, $C_0$ coarse geometry and scalar curvature, J. Funct. Anal. 197 (2003) 469 MR1960422
41 N Wright, The coarse Baum–Connes conjecture via $C_0$ coarse geometry, J. Funct. Anal. 220 (2005) 265 MR2119281
42 G L Yu, Coarse Baum–Connes conjecture, $K$–Theory 9 (1995) 199 MR1344138