Algebraic & Geometric Topology Volume 10, issue 4 (2010)

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The Whitehead group and the lower algebraic $K$–theory of braid groups on $\mathbb{S}^2$ and $\mathbb{R}P^2$

Daniel Juan-Pineda and Silvia Millan-López

Algebraic & Geometric Topology 10 (2010) 1887–1903

DOI: 10.2140/agt.2010.10.1887

Bibliography

1	D R Anderson, W C Hsiang, The functors $K_{-i}$ and pseudo-isotopies of polyhedra, Ann. of Math. $(2)$ 105 (1977) 201 MR0440573
2	C S Aravinda, F T Farrell, S K Roushon, Algebraic $K$–theory of pure braid groups, Asian J. Math. 4 (2000) 337 MR1797585
3	H Bass, Algebraic $K$–theory, W. A. Benjamin (1968) MR0249491
4	E Berkove, D Juan-Pineda, Q Lu, Algebraic $K$–theory of mapping class groups, $K$–Theory 32 (2004) 83 MR2079607
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	J van Buskirk, Braid groups of compact $2$–manifolds with elements of finite order, Trans. Amer. Math. Soc. 122 (1966) 81 MR0189013
7	D W Carter, Lower $K$–theory of finite groups, Comm. Algebra 8 (1980) 1927 MR590500
8	F Cohen, J Pakianathan, Notes on configuration spaces and braid groups (1999)
9	C W Curtis, I Reiner, Methods of representation theory. Vol. II. With applications to finite groups and orders, Pure and Applied Math., Wiley (1987) MR892316
10	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
11	E Fadell, L Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111 MR0141126
12	E Fadell, J Van Buskirk, The braid groups of $E^{2}$ and $S^{2}$, Duke Math. J. 29 (1962) 243 MR0141128
13	F T Farrell, L E Jones, Isomorphism conjectures in algebraic $K$–theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537
14	F T Farrell, S K Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices (2000) 515 MR1759505
15	D L Gonçalves, J Guaschi, The braid groups of the projective plane, Algebr. Geom. Topol. 4 (2004) 757 MR2100679
16	D L Gonçalves, J Guaschi, The braid groups of the projective plane and the Fadell–Neuwirth short exact sequence, Geom. Dedicata 130 (2007) 93 MR2365780
17	D L Gonçalves, J Guaschi, Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane, J. Group Theory 13 (2010) 277 MR2607582
18	D Juan-Pineda, S Millan-López, Invariants associated to the pure braid group of the sphere, Bol. Soc. Mat. Mexicana $(3)$ 12 (2006) 27 MR2301740
19	D Juan-Pineda, S Millan-López, The braid groups of $\mathbb{R}P^2$ satisfy the fibered isomorphism conjecture, from: "Cohomology of groups and algebraic $K$–theory" (editors L Ji, K Liu, S T Yau), Adv. Lectures in Math. 12, International Press (2010) 187
20	M E Keating, On the $K$–theory of the quaternion group, Mathematika 20 (1973) 59 MR0340379
21	J F Lafont, I J Ortiz, Relating the Farrell Nil-groups to the Waldhausen Nil-groups, Forum Math. 20 (2008) 445 MR2418200
22	J Martinet, Modules sur l'algèbre du groupe quaternionien, Ann. Sci. École Norm. Sup. $(4)$ 4 (1971) 399 MR0291208
23	R Oliver, Whitehead groups of finite groups, London Math. Soc. Lecture Note Ser. 132, Cambridge Univ. Press (1988) MR933091
24	F Quinn, Ends of maps. II, Invent. Math. 68 (1982) 353 MR669423
25	J P Serre, Linear representations of finite groups, Graduate Texts in Math. 42, Springer (1977) MR0450380
26	J P Serre, Trees, Springer Monogr. in Math., Springer (2003) MR1954121
27	C T C Wall, Poincaré complexes. I, Ann. of Math. $(2)$ 86 (1967) 213 MR0217791