Algebraic & Geometric Topology Volume 16, issue 4 (2016)

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On the algebraic K-theory of the Hilbert modular group

Mauricio Bustamante and Luis Jorge Sánchez Saldaña

Algebraic & Geometric Topology 16 (2016) 2107–2125

DOI: 10.2140/agt.2016.16.2107

Bibliography

1	A Alves, P Ontaneda, A formula for the Whitehead group of a three-dimensional crystallographic group, Topology 45 (2006) 1 MR2170492
2	H Bass, The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups, Topology 4 (1965) 391 MR0193120
3	E Berkove, F T Farrell, D Juan-Pineda, K Pearson, The Farrell–Jones isomorphism conjecture for finite covolume hyperbolic actions and the algebraic K-theory of Bianchi groups, Trans. Amer. Math. Soc. 352 (2000) 5689 MR1694279
4	E Berkove, D Juan-Pineda, K Pearson, The lower algebraic K-theory of Fuchsian groups, Comment. Math. Helv. 76 (2001) 339 MR1839350
5	E Berkove, D Juan-Pineda, K Pearson, A geometric approach to the lower algebraic K-theory of Fuchsian groups, Topology Appl. 119 (2002) 269 MR1888672
6	M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic K-theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
7	D W Carter, Lower K-theory of finite groups, Comm. Algebra 8 (1980) 1927 MR590500
8	J F Davis, Q Khan, A Ranicki, Algebraic K-theory over the infinite dihedral group : an algebraic approach, Algebr. Geom. Topol. 11 (2011) 2391 MR2835234
9	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
10	J F Davis, W Lück, The p–chain spectral sequence, K-Theory 30 (2003) 71 MR2061848
11	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
12	D S Farley, I J Ortiz, Algebraic K-theory of crystallographic groups : the three-dimensional splitting case, 2113, Springer (2014) MR3308161
13	F T Farrell, L E Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537
14	E Freitag, Hilbert modular forms, Springer-Verlag (1990) MR1050763
15	G van der Geer, Hilbert modular surfaces, 16, Springer (1988) MR930101
16	J Grunewald, The behavior of Nil-groups under localization and the relative assembly map, Topology 47 (2008) 160 MR2414359
17	F E P Hirzebruch, Hilbert modular surfaces, Enseignement Math. 19 (1973) 183 MR0393045
18	B Jahren, Involutions on the rational K-theory of group rings of finite groups, from: "Alpine perspectives on algebraic topology" (editors C Ausoni, K Hess, J Scherer), Contemp. Math. 504, Amer. Math. Soc. (2009) 189 MR2581909
19	D Juan-Pineda, J F Lafont, S Millan-Vossler, S Pallekonda, Algebraic K-theory of virtually free groups, Proc. Roy. Soc. Edinburgh Sect. A 141 (2011) 1295 MR2855898
20	D Juan-Pineda, S Millan-López, Invariants associated to the pure braid group of the sphere, Bol. Soc. Mat. Mexicana 12 (2006) 27 MR2301740
21	D Juan-Pineda, S Millan-López, The Whitehead group and the lower algebraic K-theory of braid groups on 𝕊² and ℝℙ², Algebr. Geom. Topol. 10 (2010) 1887 MR2728479
22	D Juan-Pineda, L J Sánchez Saldaña, On the ranks of the algebraic K-theory of hyperbolic groups, Bol. Soc. Mat. Mex. 20 (2014) 277 MR3264616
23	H Kammeyer, W Lück, H Rüping, The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups, Geom. Topol. 20 (2016) 1275 MR3523058
24	J F Lafont, I J Ortiz, Lower algebraic K-theory of hyperbolic 3–simplex reflection groups, Comment. Math. Helv. 84 (2009) 297 MR2495796
25	W Lück, R Stamm, Computations of K- and L-theory of cocompact planar groups, K-Theory 21 (2000) 249 MR1803230
26	R Oliver, Whitehead groups of finite groups, 132, Cambridge Univ. Press (1988) MR933091
27	K Pearson, Algebraic K-theory of two-dimensional crystallographic groups, K-Theory 14 (1998) 265 MR1633509
28	E K Pedersen, C A Weibel, A nonconnective delooping of algebraic K-theory, from: "Algebraic and geometric topology", Lecture Notes in Math. 1126, Springer (1985) 166
29	A Prestel, Die elliptischen Fixpunkte der Hilbertschen Modulgruppen, Math. Ann. 177 (1968) 181 MR0228439
30	F Waldhausen, Algebraic K-theory of generalized free products, II, Ann. of Math. (2) 108 (1978) 205 MR0498808