Algebraic & Geometric Topology Volume 14, issue 4 (2014)

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Equivariant principal bundles and their classifying spaces

Wolfgang Lück and Bernardo Uribe

Algebraic & Geometric Topology 14 (2014) 1925–1995

DOI: 10.2140/agt.2014.14.1925

Bibliography

1	H Abels, A universal proper $G$–space, Math. Z. 159 (1978) 143 MR0501039
2	M F Atiyah, $K$–theory and reality, Quart. J. Math. Oxford Ser. 17 (1966) 367 MR0206940
3	M F Atiyah, Algebraic topology and operators in Hilbert space, from: "Lectures in Modern Analysis and Applications, I" (editor C T Taam), Springer (1969) 101 MR0248803
4	M F Atiyah, G B Segal, Twisted $K$–theory, Ukr. Mat. Visn. 1 (2004) 287 MR2172633
5	T Barcenas, J Espinoza, M Joachim, B Uribe, Classification of twists in equivariant $K$–theory for proper and discrete group actions, Proc. Lond. Math. Soc. (2013)
6	G Birkhoff, A note on topological groups, Compositio Math. 3 (1936) 427 MR1556955
7	T tom Dieck, Transformation groups, Studies in Mathematics 8, de Gruyter (1987) MR889050
8	S A Gaal, Linear analysis and representation theory, Grundlehren der Math. Wissenschaften 198, Springer (1973) MR0447465
9	I Hambleton, J C Hausmann, Equivariant principal bundles over spheres and cohomogeneity one manifolds, Proc. London Math. Soc. 86 (2003) 250 MR1971468
10	P de la Harpe, Classical Banach–Lie algebras and Banach–Lie groups of operators in Hilbert space, Lecture Notes in Mathematics 285, Springer, Berlin (1972)
11	D Husemoller, Fibre bundles, McGraw-Hill Book Co. (1966) MR0229247
12	S Illman, Existence and uniqueness of equivariant triangulations of smooth proper $G$–manifolds with some applications to equivariant Whitehead torsion, J. Reine Angew. Math. 524 (2000) 129 MR1770606
13	K Jänich, Vektorraumbündel und der Raum der Fredholm–Operatoren, Math. Ann. 161 (1965) 129 MR0190946
14	S Kakutani, Über die Metrisation der topologischen Gruppen, Proc. Imp. Acad. 12 (1936) 82 MR1568424
15	N Kitchloo, Dominant $K$–theory and integrable highest weight representations of Kac–Moody groups, Adv. Math. 221 (2009) 1191 MR2518636
16	N H Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965) 19 MR0179792
17	S Lang, Differential manifolds, Addison-Wesley (1972) MR0431240
18	R K Lashof, Equivariant bundles, Illinois J. Math. 26 (1982) 257 MR650393
19	R K Lashof, J P May, Generalized equivariant bundles, Bull. Soc. Math. Belg. Sér. A 38 (1986) 265 MR885537
20	R K Lashof, J P May, G B Segal, Equivariant bundles with abelian structural group, from: "Proceedings of the Northwestern Homotopy Theory Conference" (editors H R Miller, S B Priddy), Contemp. Math. 19, Amer. Math. Soc. (1983) 167 MR711050
21	D H Lee, T S Wu, On conjugacy of homomorphisms of topological groups, II, Illinois J. Math. 14 (1970) 409 MR0267037
22	W Lück, Transformation groups and algebraic $K$–theory, Lecture Notes in Mathematics 1408, Springer, Berlin (1989) MR1027600
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	J P May, Some remarks on equivariant bundles and classifying spaces, from: "International Conference on Homotopy Theory", Astérisque 191, Soc. Math. France (1990) 7, 239 MR1098973
25	H Miyazaki, The paracompactness of $\mathit{CW}$–complexes, Tôhoku Math. J. 4 (1952) 309 MR0054246
26	P S Mostert, Local cross sections in locally compact groups, Proc. Amer. Math. Soc. 4 (1953) 645 MR0056614
27	J R Munkres, Topology: A first course, Prentice-Hall (1975) MR0464128
28	M Murayama, K Shimakawa, Universal equivariant bundles, Proc. Amer. Math. Soc. 123 (1995) 1289 MR1231040
29	K H Neeb, Towards a Lie theory of locally convex groups, Jpn. J. Math. 1 (2006) 291 MR2261066
30	R S Palais, On the existence of slices for actions of noncompact Lie groups, Ann. of Math. 73 (1961) 295 MR0126506
31	G B Segal, Cohomology of topological groups, from: "Symposia Mathematica, Vol. IV", Academic Press (1970) 377 MR0280572
32	D J Simms, Topological aspects of the projective unitary group, Proc. Cambridge Philos. Soc. 68 (1970) 57 MR0261394
33	N E Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133 MR0210075