Algebraic & Geometric Topology Volume 26, issue 1 (2026)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Bernoulli shifts on additive categories and algebraic $K$-theory of wreath products

Julian Kranz and Shintaro Nishikawa

Algebraic & Geometric Topology 26 (2026) 321–347

DOI: 10.2140/agt.2026.26.321

Bibliography

1	A Bartels, M Bestvina, The Farrell–Jones conjecture for mapping class groups, Invent. Math. 215 (2019) 651 MR3910072
2	A Bartels, W Lück, On crossed product rings with twisted involutions, their module categories and L-theory, from: "Cohomology of groups and algebraic K-theory" (editors L Ji, K Liu, S T Yau), Adv. Lect. Math. 12, International (2010) 1 MR2655174
3	A Bartels, W Lück, The Borel conjecture for hyperbolic and CAT(0)-groups, Ann. of Math. (2) 175 (2012) 631 MR2993750
4	A Bartels, W Lück, H Reich, The K-theoretic Farrell–Jones conjecture for hyperbolic groups, Invent. Math. 172 (2008) 29 MR2385666
5	A Bartels, W Lueck, Vanishing of Nil-terms and negative K-theory for additive categories, preprint (2022) arXiv:2002.03412v4
6	A Bartels, H Reich, Coefficients for the Farrell–Jones conjecture, Adv. Math. 209 (2007) 337 MR2294225
7	C Barwick, S Glasman, A Mathew, T Nikolaus, K-theory and polynomial functors, (2021) arXiv:2102.00936
8	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
9	A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K-theory, Geom. Topol. 17 (2013) 733 MR3070515
10	J Chabert, S Echterhoff, H Oyono-Oyono, Going-down functors, the Künneth formula, and the Baum–Connes conjecture, Geom. Funct. Anal. 14 (2004) 491 MR2100669
11	S Chakraborty, S Echterhoff, J Kranz, S Nishikawa, K-theory of noncommutative Bernoulli shifts, Math. Ann. 388 (2024) 2671 MR4705749
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, F Quinn, H Reich, Algebraic K-theory over the infinite dihedral group : a controlled topology approach, J. Topol. 4 (2011) 505 MR2832565
14	E Ellis, Equivariant algebraic kk-theory and adjointness theorems, J. Algebra 398 (2014) 200 MR3123759
15	F T Farrell, L E Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537
16	M P Gomez Aparicio, P Julg, A Valette, The Baum–Connes conjecture : an extended survey, from: "Advances in noncommutative geometry—on the occasion of Alain Connes’ 70th birthday" (editors A Chamseddine, C Consani, N Higson, M Khalkhali, H Moscovici, G Yu), Springer (2019) 127 MR4300553
17	J Grunewald, The behavior of Nil-groups under localization and the relative assembly map, Topology 47 (2008) 160 MR2414359
18	K Hilman, Parametrised noncommutative motives and equivariant cubical descent in algebraic K-theory, (2022) arXiv:2202.02591
19	M Izumi, The K-theory of the flip automorphisms, from: "Operator algebras and mathematical physics" (editors M Izumi, Y Kawahigashi, H Matui, N Ozawa), Adv. Stud. Pure Math. 80, Math. Soc. Japan (2019) 123 MR3966586
20	G G Kasparov, Equivariant KK-theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
21	J Kranz, S Nishikawa, Equivariant KK-theory of Bernoulli shifts on C^∗-algebras with approximately inner flip, (2022) arXiv:2210.00061
22	X Li, K-theory for generalized Lamplighter groups, Proc. Amer. Math. Soc. 147 (2019) 4371 MR4002549
23	W Lück, Isomorphism conjectures in K- and L-theory, Springer (2025)
24	W Lück, W Steimle, Non-connective K- and Nil-spectra of additive categories, from: "An alpine expedition through algebraic topology" (editors C Ausoni, K Hess, B Johnson, W Lück, J Scherer), Contemp. Math. 617, Amer. Math. Soc. (2014) 205 MR3243400
25	W Lück, W Steimle, A twisted Bass–Heller–Swan decomposition for the algebraic K-theory of additive categories, Forum Math. 28 (2016) 129 MR3441110
26	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
27	H Reich, M Varisco, Algebraic K-theory, assembly maps, controlled algebra, and trace methods, from: "Space–time–matter" (editors J Brüning, M Staudacher), De Gruyter (2018) 1 MR3792301
28	A S Toms, W Winter, Strongly self-absorbing C^∗-algebras, Trans. Amer. Math. Soc. 359 (2007) 3999 MR2302521