Homotopy representations of finite groups

Tom Dieck, Tammo; Petrie, Ted

Tom Dieck, Tammo ; Petrie, Ted

Publications Mathématiques de l'IHÉS, Tome 56 (1982), pp. 129-169.

MR Zbl

@article{PMIHES_1982__56__129_0,
     author = {Tom Dieck, Tammo and Petrie, Ted},
     title = {Homotopy representations of finite groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {129--169},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {56},
     year = {1982},
     mrnumber = {86b:57020},
     zbl = {0507.57025},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1982__56__129_0/}
}

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%A Petrie, Ted
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%J Publications Mathématiques de l'IHÉS
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Tom Dieck, Tammo; Petrie, Ted. Homotopy representations of finite groups. Publications Mathématiques de l'IHÉS, Tome 56 (1982), pp. 129-169. http://archive.numdam.org/item/PMIHES_1982__56__129_0/

Bibliographie
Cité par

[1] Borel (A.), Fixed point theorems for elementary commutative groups, in Seminar on transformation groups, Annals of Math. Studies, 43, Princeton Univ. Press, 1960.

[2] Bredon (G. E.), Introduction to compact transformation groups, Academic Press, New York, London, 1972. | MR | Zbl

[3] Bredon (G. E.), Fixed point sets of actions on Poincaré duality spaces, Topology, 12 (1973), 159-175. | MR | Zbl

[4] Tom Dieck (T.), The Burnside ring of a compact Lie group I, Math. Ann., 215 (1975), 235-250. | MR | Zbl

[5] Tom Dieck (T.), Homotopy-equivalent group representations, Journal f. d. reine u. angew. Math., 298 (1978), 182-195. | MR | Zbl

[6] Tom Dieck (T.), Homotopy equivalent group representations and Picard groups of the Burnside ring and the character ring, Manuscripta math., 26 (1978), 179-200. | MR | Zbl

[7] Tom Dieck (T.), Semi-linear group actions on spheres: Dimension functions, in Proceedings Conf. Algebrai, Topology, Aarhus, 1978, Springer Lecture Notes, 763 (1979), 448-457. | MR | Zbl

[8] Tom Dieck (T.), Transformation groups and representation theory, Springer Lecture Notes, 766 (1979). | MR | Zbl

[9] Tom Dieck (T.) and Petrie (T.), Geometric modules over the Burnside ring, Inventiones math., 47 (1978)c 273-287. | MR | Zbl

[10] Tom Dieck (T.) and Petrie (T.), The homotopy structure of finite group actions on spheres, in Proceedings Conf. Algebraic Topology, Waterloo, 1978, Springer Lecture Notes, 741 (1979), 222-243. | MR | Zbl

[11] Dress (A.), Contributions to the theory of induced representations, in Batelle Institute Conference on Algebraic K-Theory II, Springer Lecture Notes, 342 (1973), 183-240. | MR | Zbl

[12] Hauschild (H.), Äquivariante Homotopie I, Arch. Math., 29 (1977), 158-165. | MR | Zbl

[13] Hauschild (H.), Äquivariante Whitehead Torsion, Manuscripta math., 26 (1978), 63-82. | MR | Zbl

[14] Huppert (H.), Endliche Gruppen I, Springer, Berlin, Heidelberg, New York, 1967. | Zbl

[15] Illman (S.), Smooth equivariant triangulations of G-manifolds for G a finite group, Math. Ann., 233 (1978), 199-220. | MR | Zbl

[16] James (I. M.) and Segal (G. B.), On equivariant homotopy type, Topology, 17 (1978), 267-272. | MR | Zbl

[17] Lang (S.), Algebra, Addison-Wesley, Reading, 1965. | MR | Zbl

[18] Milnor (J.), Singular points of complex hypersurfaces, Annals of Math. Studies, 61, Princeton Univ. Press, 1968. | MR | Zbl

[19] Petrie (T.), G-maps and the projective class group, Comment. math. Helv., 51 (1976), 611-626. | MR | Zbl

[20] Petrie (T.), G-surgery, I. A Survey, in Proceedings Conf. Algebraic and Geometric Topology, Santa Barbara, 1977, Springer Lecture Notes, 664 (1978), 197-233. | MR | Zbl

[21] Rim (D. S.), Modules over finite groups, Ann. of Math., 69 (1959), 700-712. | MR | Zbl

[22] Swan (R. G.), Induced representations and projective modules, Ann. of Math., 71 (1960), 552-578. | MR | Zbl

[23] Swan (R. G.), Periodic resolutions for finite groups, Ann. of Math., 72 (1960), 267-291. | MR | Zbl

[24] Swan (R. G.) and Evans (E. G.), K-theory of finite groups and orders, Springer Lecture Notes, 149 (1970). | MR | Zbl

[25] Taylor (M. J.), Locallyfree class groups of groups of prime power order, Journal of Algebra, 50 (1978), 463-487. | MR | Zbl

[26] Wall (C. T. C.), Finiteness conditions for CW-complexes, Ann. of Math., 81 (1965), 56-69. | MR | Zbl

[27] Wirthmüller (K.), Equivariant S-duality, Arch. Math., 26 (1975), 427-431. | MR | Zbl

[28] Wolf (J. A.), Spaces of constant curvature, McGraw-Hill, New York, 1967. | MR | Zbl

[29] Tom Dieck (T.), Über projektive Moduln und Endlichkeitshindernisse bei Transformationsgruppen, Manuscripta math., 24 (1981), 135-155. | MR | Zbl

[30] Dovermann (K. H.) and Petrie (T.), Artin relation for smooth representations, Proc. Nat. Acad. Sci. U.S.A., 177 (1980), 5620-5621. | MR | Zbl

[31] Petrie (T.), Free metacyclic group actions on homotopy spheres, Ann. of Math., 94 (1971), 108-124. | MR | Zbl

[32] Segal (G.), Equivariant stable homotopy, in Proc. Congrès intern. Math. Nice, 1970, t. 2, 59-63. | MR | Zbl

[33] Illman (S.), Equivariant algebraic topology, Thesis, Princeton, 1972.

[34] Tom Dieck (T.), Homotopiedarstellungen endlicher Gruppen : Dimensionsfunktionen, Inventiones math., 67 (1982), 231-252. | MR | Zbl