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Smith equivalence and finite Oliver groups with Laitinen number 0 or 1

Krzysztof Pawałowski and Ronald Solomon

Algebraic & Geometric Topology 2 (2002) 843–895
Bibliography
1 M F Atiyah, R Bott, A Lefschetz fixed point formula for elliptic complexes. II. Applications, Ann. of Math. $(2)$ 88 (1968) 451 MR0232406
2 A Bak, M Morimoto, $K$–theoretic groups with positioning map and equivariant surgery, Proc. Japan Acad. Ser. A Math. Sci. 70 (1994) 6 MR1272660
3 A Bak, M Morimoto, Equivariant surgery with middle-dimensional singular sets. I, Forum Math. 8 (1996) 267 MR1387697
4 W Bannuscher, G Tiedt, On a theorem of Deaconescu, Rostock. Math. Kolloq. (1994) 23 MR1304866
5 G E Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics 46, Academic Press (1972) MR0413144
6 S E Cappell, J L Shaneson, Fixed points of periodic maps, Proc. Nat. Acad. Sci. U.S.A. 77 (1980) 5052 MR587279
7 S E Cappell, J L Shaneson, Fixed points of periodic differentiable maps, Invent. Math. 68 (1982) 1 MR666635
8 S E Cappell, J L Shaneson, Representations at fixed points, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 151 MR780963
9 E C Cho, Smith equivalent representations of generalized quaternion groups, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 317 MR780970
10 E C Cho, D Y Suh, Induction in equivariant $K$–theory and $s$–Smith equivalence of representations, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 311 MR780969
11 J H Conway, R T Curtis, S P Norton, R A Parker, R A Wilson, Atlas of finite groups: Maximal subgroups and ordinary characters for simple groups, Oxford University Press (1985) MR827219
12 C W Curtis, I Reiner, Methods of representation theory Vol I, Pure and Applied Mathematics, John Wiley & Sons (1981) MR632548
13 C W Curtis, I Reiner, Methods of representation theory Vol II, Pure and Applied Mathematics, John Wiley & Sons (1987) MR892316
14 A L Delgado, Y F Wu, On locally finite groups in which every element has prime power order, Illinois J. Math. 46 (2002) 885 MR1951246
15 T tom Dieck, Transformation groups, de Gruyter Studies in Mathematics 8, Walter de Gruyter & Co. (1987) MR889050
16 K H Dovermann, M Herzog, Gap conditions for representations of symmetric groups, J. Pure Appl. Algebra 119 (1997) 113 MR1453215
17 K H Dovermann, T Petrie, Smith equivalence of representations for odd order cyclic groups, Topology 24 (1985) 283 MR815481
18 K H Dovermann, T Petrie, R Schultz, Transformation groups and fixed point data, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 159 MR780964
19 K H Dovermann, D Y Suh, Smith equivalence for finite abelian groups, Pacific J. Math. 152 (1992) 41 MR1139972
20 K H Dovermann, L C Washington, Relations between cyclotomic units and Smith equivalence of representations, Topology 28 (1989) 81 MR991100
21 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups, Mathematical Surveys and Monographs 40, American Mathematical Society (1994) MR1303592
22 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups. Number 2. Part I. Chapter G: General group theory, Mathematical Surveys and Monographs 40, American Mathematical Society (1996) MR1358135
23 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups. Number 3. Part I. Chapter A: Almost simple $K$–groups, Mathematical Surveys and Monographs 40, American Mathematical Society (1998) MR1490581
24 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups. Number 4. Part II. Chapters 1–4: Uniqueness theorems, Mathematical Surveys and Monographs 40, American Mathematical Society (1999) MR1675976
25 D Gorenstein, R Lyons, R Solomon, The classification of the finite simple groups. Number 5. Part III. Chapters 1–6: The generic case, stages 1–3a, Mathematical Surveys and Monographs 40, American Mathematical Society (2002) MR1923000
26 G Higman, Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957) 335 MR0089205
27 B Huppert, N Blackburn, Finite groups II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (1982) MR650245
28 S Illman, Representations at fixed points of actions of finite groups on spheres, from: "Current trends in algebraic topology, Part 2 (London, Ont., 1981)", CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 135 MR686142
29 G James, M Liebeck, Representations and characters of groups, Cambridge University Press (2001) MR1864147
30 K Kawakubo, The theory of transformation groups, The Clarendon Press Oxford University Press (1991) MR1150492
31 E Laitinen, M Morimoto, K Pawałowski, Deleting-inserting theorem for smooth actions of finite nonsolvable groups on spheres, Comment. Math. Helv. 70 (1995) 10 MR1314939
32 E Laitinen, M Morimoto, Finite groups with smooth one fixed point actions on spheres, Forum Math. 10 (1998) 479 MR1631012
33 E Laitinen, K Pawałowski, Smith equivalence of representations for finite perfect groups, Proc. Amer. Math. Soc. 127 (1999) 297 MR1468195
34 M Masuda, T Petrie, Lectures on transformation groups and Smith equivalence, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 191 MR780965
35 J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR0196736
36 M Morimoto, Bak groups and equivariant surgery, $K$–Theory 2 (1989) 465 MR990572
37 M Morimoto, Bak groups and equivariant surgery II, $K$–Theory 3 (1990) 505 MR1071893
38 M Morimoto, Equivariant surgery theory: deleting-inserting theorems of fixed point manifolds on spheres and disks, $K$–Theory 15 (1998) 13 MR1643619
39 M Morimoto, K Pawałowski, Equivariant wedge sum construction of finite contractible $G$–CW complexes with $G$–vector bundles, Osaka J. Math. 36 (1999) 767 MR1745658
40 M Morimoto, K Pawałowski, The equivariant bundle subtraction theorem and its applications, Fund. Math. 161 (1999) 279 MR1716021
41 M Morimoto, K Pawałowski, Smooth actions of finite Oliver groups on spheres, Topology 42 (2003) 395 MR1941442
42 M Morimoto, T Sumi, M Yanagihara, Finite groups possessing gap modules, from: "Geometry and topology: Aarhus (1998)", Contemp. Math. 258, Amer. Math. Soc. (2000) 329 MR1778115
43 R Oliver, Fixed-point sets of group actions on finite acyclic complexes, Comment. Math. Helv. 50 (1975) 155 MR0375361
44 R Oliver, Smooth compact Lie group actions on disks, Math. Z. 149 (1976) 79 MR0423390
45 B Oliver, Fixed point sets and tangent bundles of actions on disks and Euclidean spaces, Topology 35 (1996) 583 MR1396768
46 K Pawałowski, Group actions with inequivalent representations at fixed points, Math. Z. 187 (1984) 29 MR753418
47 K Pawałowski, Fixed point sets of smooth group actions on disks and Euclidean spaces, Topology 28 (1989) 273 MR1014462
48 K Pawałowski, Smith equivalence of group modules and the Laitinen conjecture. A survey, from: "Geometry and topology: Aarhus (1998)", Contemp. Math. 258, Amer. Math. Soc. (2000) 343 MR1778116
49 T Petrie, Pseudoequivalences of $G$–manifolds, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 169 MR520505
50 T Petrie, Three theorems in transformation groups, from: "Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978)", Lecture Notes in Math. 763, Springer (1979) 549 MR561238
51 T Petrie, The equivariant $J$ homomorphism and Smith equivalence of representations, from: "Current trends in algebraic topology, Part 2 (London, Ont., 1981)", CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 223 MR686148
52 T Petrie, Smith equivalence of representations, Math. Proc. Cambridge Philos. Soc. 94 (1983) 61 MR704803
53 T Petrie, J Randall, Spherical isotropy representations, Inst. Hautes Études Sci. Publ. Math. (1985) 221 MR823175
54 C U Sanchez, Actions of groups of odd order on compact, orientable manifolds, Proc. Amer. Math. Soc. 54 (1976) 445 MR0407871
55 , Problems submitted to the AMS summer research conference on group actions, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 513 MR780979
56 P A Smith, New results and old problems in finite transformation groups, Bull. Amer. Math. Soc. 66 (1960) 401 MR0125581
57 D Y Suh, $s$–Smith equivalent representations of finite abelian groups, from: "Group actions on manifolds (Boulder, Colo., 1983)", Contemp. Math. 36, Amer. Math. Soc. (1985) 323 MR780971
58 T Sumi, Gap modules for direct product groups, J. Math. Soc. Japan 53 (2001) 975 MR1852892
59 T Sumi, Gap modules for semidirect product groups, Kyushu J. Math. 58 (2004) 33 MR2053718
60 M Suzuki, On a class of doubly transitive groups, Ann. of Math. $(2)$ 75 (1962) 105 MR0136646