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On the equivariant $K$– and $KO$–homology of some special linear groups

Sam Hughes

Algebraic & Geometric Topology 21 (2021) 3483–3512
Bibliography
1 A Adem, N Naffah, On the cohomology of SL2([1∕p]), from: "Geometry and cohomology in group theory" (editors P H Kropholler, G A Niblo, R Stöhr), Lond. Math. Soc. Lect. Note Ser. 252, Cambridge Univ. Press (1998) 1 MR1709948
2 M P G Aparicio, P Julg, A Valette, The Baum–Connes conjecture : an extended survey, from: "Advances in noncommutative geometry" (editors A Chamseddine, C Consani, N Higson, M Khalkhali, H Moscovici, G Yu), Springer (2019) 127
3 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
4 P Baum, M Karoubi, On the Baum–Connes conjecture in the real case, Q. J. Math. 55 (2004) 231 MR2082090
5 B Bekka, P de la Harpe, A Valette, Kazhdan’s property (T), 11, Cambridge Univ. Press (2008) MR2415834
6 B Botvinnik, P Gilkey, S Stolz, The Gromov–Lawson–Rosenberg conjecture for groups with periodic cohomology, J. Differential Geom. 46 (1997) 374 MR1484887
7 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
8 R R Bruner, J P C Greenlees, Connective real K–theory of finite groups, 169, Amer. Math. Soc. (2010) MR2723113
9 A T Bui, G Ellis, The homology of SL2([1∕m]) for small m, J. Algebra 408 (2014) 102 MR3197173
10 A T Bui, A D Rahm, M Wendt, The Farrell–Tate and Bredon homology for PSL4() via cell subdivisions, J. Pure Appl. Algebra 223 (2019) 2872 MR3912952
11 M Bustamante, L J Sánchez Saldaña, On the algebraic K–theory of the Hilbert modular group, Algebr. Geom. Topol. 16 (2016) 2107 MR3546460
12 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
13 J F Davis, W Lück, The p–chain spectral sequence, K–Theory 30 (2003) 71 MR2061848
14 J F Davis, W Lück, The topological K–theory of certain crystallographic groups, J. Noncommut. Geom. 7 (2013) 373 MR3054301
15 J F Davis, K Pearson, The Gromov–Lawson–Rosenberg conjecture for cocompact Fuchsian groups, Proc. Amer. Math. Soc. 131 (2003) 3571 MR1991770
16 D Degrijse, I J Leary, Equivariant vector bundles over classifying spaces for proper actions, Algebr. Geom. Topol. 17 (2017) 131 MR3604375
17 R Flores, S Pooya, A Valette, K–homology and K–theory for the lamplighter groups of finite groups, Proc. Lond. Math. Soc. 115 (2017) 1207 MR3741850
18 M Fuentes-Rumí, The equivariant K– and KO–theory of certain classifying spaces via an equivariant Atiyah–Hirzebruch spectral sequence, preprint (2019) arXiv:1905.02972
19 W Fulton, J Harris, Representation theory: a first course, 129, Springer (1991) MR1153249
20 H W Henn, The cohomology of SL(3, [12]), K–Theory 16 (1999) 299 MR1683179
21 N Higson, G Kasparov, Operator K–theory for groups which act properly and isometrically on Hilbert space, Electron. Res. Announc. Amer. Math. Soc. 3 (1997) 131 MR1487204
22 N Higson, V Lafforgue, G Skandalis, Counterexamples to the Baum–Connes conjecture, Geom. Funct. Anal. 12 (2002) 330 MR1911663
23 S Hughes, Cohomology of Fuchsian groups and non-euclidean crystallographic groups, preprint (2019) arXiv:1910.00519
24 S Hughes, Equivariant cohomology, lattices, and trees, PhD thesis, University of Southampton (2021)
25 M Joachim, T Schick, Positive and negative results concerning the Gromov–Lawson–Rosenberg conjecture, from: "Geometry and topology" (editors K Grove, I H Madsen, E K Pedersen), Contemp. Math. 258, Amer. Math. Soc. (2000) 213 MR1778107
26 G G Kasparov, Operator K–theory and its applications, Itogi Nauki Tekh. 27 (1985) 3
27 G G Kasparov, Equivariant KK–theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
28 S Katok, Fuchsian groups, Univ. Chicago Press (1992) MR1177168
29 S Kwasik, R Schultz, Positive scalar curvature and periodic fundamental groups, Comment. Math. Helv. 65 (1990) 271 MR1057244
30 J F Lafont, I J Ortiz, A D Rahm, R J Sánchez-García, Equivariant K–homology for hyperbolic reflection groups, Q. J. Math. 69 (2018) 1475 MR3908707
31 X Li, K–theory for generalized lamplighter groups, Proc. Amer. Math. Soc. 147 (2019) 4371 MR4002549
32 W Lück, R Stamm, Computations of K– and L–theory of cocompact planar groups, K–Theory 21 (2000) 249 MR1803230
33 A M Macbeath, The classification of non-euclidean plane crystallographic groups, Canadian J. Math. 19 (1967) 1192 MR220838
34 M Matthey, H Oyono-Oyono, W Pitsch, Homotopy invariance of higher signatures and 3–manifold groups, Bull. Soc. Math. France 136 (2008) 1 MR2415334
35 G Mislin, A Valette, Proper group actions and the Baum–Connes conjecture, Birkhäuser (2003) MR2027168
36 S Pooya, K–theory and K–homology of finite wreath products with free groups, Illinois J. Math. 63 (2019) 317 MR3987499
37 S Pooya, A Valette, K–theory for the C–algebras of the solvable Baumslag–Solitar groups, Glasg. Math. J. 60 (2018) 481 MR3784059
38 A D Rahm, Homology and K–theory of the Bianchi groups, C. R. Math. Acad. Sci. Paris 349 (2011) 615 MR2817377
39 A D Rahm, On the equivariant K–homology of PSL2 of the imaginary quadratic integers, Ann. Inst. Fourier (Grenoble) 66 (2016) 1667 MR3494182
40 J Rosenberg, C–algebras, positive scalar curvature and the Novikov conjecture, II, from: "Geometric methods in operator algebras" (editors H Araki, E G Effros), Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech. (1986) 341 MR866507
41 J Rosenberg, C–algebras, positive scalar curvature, and the Novikov conjecture, III, Topology 25 (1986) 319 MR842428
42 J Rosenberg, S Stolz, Manifolds of positive scalar curvature, from: "Algebraic topology and its applications" (editors G E Carlsson, R L Cohen, W C Hsiang, J D S Jones), Math. Sci. Res. Inst. Publ. 27, Springer (1994) 241 MR1268192
43 R J Sánchez-García, Equivariant K–homology of the classifying space for proper actions, PhD thesis, University of Southampton (2005) MR2715961
44 R J Sánchez-García, Equivariant K–homology for some Coxeter groups, J. Lond. Math. Soc. 75 (2007) 773 MR2352735
45 R Sánchez-García, Bredon homology and equivariant K–homology of SL(3, ), J. Pure Appl. Algebra 212 (2008) 1046 MR2387584
46 L J Sánchez Saldaña, On the dimension of groups that satisfy certain conditions on their finite subgroups, Glasg. Math. J. (2020)
47 L J Sánchez Saldaña, M Velásquez, The algebraic and topological K–theory of the Hilbert modular group, Homology Homotopy Appl. 20 (2018) 377 MR3835826
48 T Schick, A counterexample to the (unstable) Gromov–Lawson–Rosenberg conjecture, Topology 37 (1998) 1165 MR1632971
49 J P Serre, Trees, Springer (1980) MR607504
50 C Soulé, The cohomology of SL3(), Topology 17 (1978) 1 MR470141
51 S Stolz, Simply connected manifolds of positive scalar curvature, Ann. of Math. 136 (1992) 511 MR1189863
52 S Stolz, Positive scalar curvature metrics: existence and classification questions, from: "Proceedings of the International Congress of Mathematicians, I" (editor S D Chatterji), Birkhäuser (1995) 625 MR1403963