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Odd primary homotopy decompositions of gauge groups

Stephen D Theriault

Algebraic & Geometric Topology 10 (2010) 535–564
Bibliography
1 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
2 A Borel, F Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958) 458 MR0102800
3 R Bott, A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960) 249 MR0123330
4 F R Cohen, J A Neisendorfer, A construction of $p$–local $H$-spaces, from: "Algebraic topology, Aarhus 1982 (Aarhus, 1982)" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 351 MR764588
5 R L Cohen, R J Milgram, The homotopy type of gauge-theoretic moduli spaces, from: "Algebraic topology and its applications" (editors G E Carlsson, R L Cohen, W C Hsiang, J D S Jones), Math. Sci. Res. Inst. Publ. 27, Springer (1994) 15 MR1268186
6 M C Crabb, Fibrewise homology, Glasg. Math. J. 43 (2001) 199 MR1838625
7 M C Crabb, W A Sutherland, Counting homotopy types of gauge groups, Proc. London Math. Soc. $(3)$ 81 (2000) 747 MR1781154
8 S K Donaldson, Connections, cohomology and the intersection forms of $4$–manifolds, J. Differential Geom. 24 (1986) 275 MR868974
9 Y Félix, J Oprea, Rational homotopy of gauge groups, Proc. Amer. Math. Soc. 137 (2009) 1519 MR2465678
10 E M Friedlander, Exceptional isogenies and the classifying spaces of simple Lie groups, Ann. Math. $(2)$ 101 (1975) 510 MR0391078
11 D H Gottlieb, Applications of bundle map theory, Trans. Amer. Math. Soc. 171 (1972) 23 MR0309111
12 B Gray, Homotopy commutativity and the $EHP$ sequence, from: "Algebraic topology (Evanston, IL, 1988)" (editors M Mahowald, S Priddy), Contemp. Math. 96, Amer. Math. Soc. (1989) 181 MR1022680
13 J Grbić, S D Theriault, Odd primary self-maps of low rank Lie groups, Canad. J. Math 62 (2010) 284
14 H Hamanaka, A Kono, Unstable $K^1$–group and homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 149 MR2217512
15 B Harris, On the homotopy groups of the classical groups, Ann. of Math. $(2)$ 74 (1961) 407 MR0131278
16 P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, North-Holland Math. Studies 15, North-Holland Publishing Co. (1975) MR0478146
17 I M James, The topology of Stiefel manifolds, London Math. Soc. Lecture Note Ser. 24, Cambridge Univ. Press (1976) MR0431239
18 D Kishimoto, A Kono, Note on mod $p$ decompositions of gauge groups, Proc. Japan Acad. Ser. A 86 (2010) 15
19 A Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295 MR1103296
20 A Kono, S Tsukuda, A remark on the homotopy type of certain gauge groups, J. Math. Kyoto Univ. 36 (1996) 115 MR1381542
21 G E Lang Jr., The evaluation map and \rmEHP sequences, Pacific J. Math. 44 (1973) 201 MR0341484
22 G Masbaum, On the cohomology of the classifying space of the gauge group over some $4$–complexes, Bull. Soc. Math. France 119 (1991) 1 MR1101938
23 M Mimura, G Nishida, H Toda, $\mathrm{Mod} p$ decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977) 627 MR0478187
24 M Mimura, H Toda, Cohomology operations and homotopy of compact Lie groups. I, Topology 9 (1970) 317 MR0266237
25 W A Sutherland, Function spaces related to gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992) 185 MR1169902
26 S Terzić, The rational topology of gauge groups and of spaces of connections, Compos. Math. 141 (2005) 262 MR2099779
27 S D Theriault, The $H$–structure of low-rank torsion free $H$-spaces, Q. J. Math. 56 (2005) 403 MR2161254
28 S D Theriault, The odd primary $H$–structure of low rank Lie groups and its application to exponents, Trans. Amer. Math. Soc. 359 (2007) 4511 MR2309196
29 H Toda, A topological proof of theorems of Bott and Borel–Hirzebruch for homotopy groups of unitary groups, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 32 (1959) 103 MR0108790
30 H Toda, On iterated suspensions. I, II, J. Math. Kyoto Univ. 5 (1966) 87, 209 MR0210130