Volume 15, issue 6 (2015)

On the $K$–theory of subgroups of virtually connected Lie groups
 1 R C Alperin, P B Shalen, Linear groups of finite cohomological dimension, Bull. Amer. Math. Soc. 4 (1981) 339 MR609046 2 A C Bartels, On the domain of the assembly map in algebraic $K$–theory, Algebr. Geom. Topol. 3 (2003) 1037 MR2012963 3 A Bartels, S Echterhoff, W Lück, Inheritance of isomorphism conjectures under colimits, from: "$K$–theory and noncommutative geometry" (editors G Cortiñas, J Cuntz, M Karoubi, R Nest, C A Weibel), Eur. Math. Soc. (2008) 41 MR2513332 4 A Bartels, F T Farrell, W Lück, The Farrell–Jones conjecture for cocompact lattices in virtually connected Lie groups, J. Amer. Math. Soc. 27 (2014) 339 MR3164984 5 A Bartels, T Farrell, L Jones, H Reich, On the isomorphism conjecture in algebraic $K$–theory, Topology 43 (2004) 157 MR2030590 6 A Bartels, W Lück, Isomorphism conjecture for homotopy $K$–theory and groups acting on trees, J. Pure Appl. Algebra 205 (2006) 660 MR2210223 7 A Bartels, W Lück, The Borel conjecture for hyperbolic and $\mathrm{CAT}(0)$–groups, Ann. of Math. 175 (2012) 631 MR2993750 8 A Bartels, W Lück, Geodesic flow for $\mathrm{CAT}(0)$–groups, Geom. Topol. 16 (2012) 1345 MR2967054 9 A Bartels, W Lück, H Reich, Equivariant covers for hyperbolic groups, Geom. Topol. 12 (2008) 1799 MR2421141 10 A Bartels, W Lück, H Reich, The $K$–theoretic Farrell–Jones conjecture for hyperbolic groups, Invent. Math. 172 (2008) 29 MR2385666 11 A Bartels, H Reich, Coefficients for the Farrell–Jones conjecture, Adv. Math. 209 (2007) 337 MR2294225 12 G Carlsson, B Goldfarb, On homological coherence of discrete groups, J. Algebra 276 (2004) 502 MR2058455 13 Y de Cornulier, Answer to “If N and G/N are virtually solvable, then G is virtually solvable?” (2013) 14 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 15 F T Farrell, L E Jones, Isomorphism conjectures in algebraic $K$–theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537 16 F T Farrell, L E Jones, The lower algebraic $K$–theory of virtually infinite cyclic groups, $K$–Theory 9 (1995) 13 MR1340838 17 L Ji, Asymptotic dimension and the integral $K$–theoretic Novikov conjecture for arithmetic groups, J. Differential Geom. 68 (2004) 535 MR2144540 18 L Ji, Integral Novikov conjectures and arithmetic groups containing torsion elements, Comm. Anal. Geom. 15 (2007) 509 MR2379803 19 H Kammeyer, W Lück, H Rüping, The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups, preprint (2014) arXiv:1401.0876v1 20 G G Kasparov, Equivariant $KK$–theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241 21 D Kasprowski, On the $K$–theory of groups with finite decomposition complexity, Proc. Lond. Math. Soc. 110 (2015) 565 MR3342098 22 W Lück, The type of the classifying space for a family of subgroups, J. Pure Appl. Algebra 149 (2000) 177 MR1757730 23 W Lück, Survey on classifying spaces for families of subgroups, from: "Infinite groups: Geometric, combinatorial and dynamical aspects" (editors L Bartholdi, T Ceccherini-Silberstein, T Smirnova-Nagnibeda, A Zuk), Progr. Math. 248, Birkhäuser (2005) 269 MR2195456 24 W Lück, H Reich, The Baum–Connes and the Farrell–Jones conjectures in $K$– and $L$–theory, from: "Handbook of $K$–theory, Vol. 1, 2" (editors E M Friedlander, D R Grayson), Springer (2005) 703 MR2181833 25 W Möhres, Torsion-free nilpotent groups with bounded ranks of the abelian subgroups, from: "Group theory" (editors O H Kegel, F Menegazzo, G Zacher), Lecture Notes in Math. 1281, Springer (1987) 115 MR921696 26 E K Pedersen, C A Weibel, A nonconnective delooping of algebraic $K$–theory, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 166 MR802790 27 G Skandalis, J L Tu, G Yu, The coarse Baum–Connes conjecture and groupoids, Topology 41 (2002) 807 MR1905840 28 R B Warfield Jr., Nilpotent groups, Lecture Notes in Mathematics 513, Springer (1976) MR0409661 29 C Wegner, The $K$–theoretic Farrell–Jones conjecture for CAT(0)–groups, Proc. Amer. Math. Soc. 140 (2012) 779 30 C Wegner, The Farrell–Jones conjecture for virtually solvable groups, preprint (2013) arXiv:1308.2432v2