Spherical isotropy representations
Publications Mathématiques de l'IHÉS, Tome 62 (1985), pp. 5-40.
@article{PMIHES_1985__62__5_0,
     author = {Petrie, Ted and Randall, John},
     title = {Spherical isotropy representations},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--40},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {62},
     year = {1985},
     zbl = {0585.57020},
     mrnumber = {823175},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1985__62__5_0/}
}
TY  - JOUR
AU  - Petrie, Ted
AU  - Randall, John
TI  - Spherical isotropy representations
JO  - Publications Mathématiques de l'IHÉS
PY  - 1985
SP  - 5
EP  - 40
VL  - 62
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1985__62__5_0/
LA  - en
ID  - PMIHES_1985__62__5_0
ER  - 
%0 Journal Article
%A Petrie, Ted
%A Randall, John
%T Spherical isotropy representations
%J Publications Mathématiques de l'IHÉS
%D 1985
%P 5-40
%V 62
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1985__62__5_0/
%G en
%F PMIHES_1985__62__5_0
Petrie, Ted; Randall, John. Spherical isotropy representations. Publications Mathématiques de l'IHÉS, Tome 62 (1985), pp. 5-40. http://www.numdam.org/item/PMIHES_1985__62__5_0/

[A1] Atiyah, M. F., Characters and cohomology, Inst. Hautes Etudes Sci. Publ. Math. No. 9 (I96I), 23-64. | Numdam | MR

[AB] Atiyah, M. F. and Bott, R., The Lefschetz fixed point theorem for Elliptic complexes II, Ann. of Math. 86 (I967), 45I-49I.

[AS] Atiyah, M. F. and Segal, G., Equivariant K-theory and completion, J. Diff. Geometry 3 (I969), I-I8. | MR | Zbl

[B1] Bredon, G., Representations at fixed points of smooth actions of compact groups, Ann. of Math. 89 (I969), 5I5-532. | MR | Zbl

[B2] Bredon, G. Introduction to transformation groups, Academic Press (I972).

[CS] Cappell, S., and Shaneson, J., Fixed points of periodic differentiable maps, Invent. Math. 68 (I982), I-I9. | MR | Zbl

[C] Cho, Eung, Thesis, Rutgers University (I984).

[Dov] Dovermann, K. H., Even dimensional Smith equivalent representations, Algebraic Topology Conf. Aarhus, Springer Lecture Notes in Math. 1051 (I982), 587-602. | MR | Zbl

[DP1] Dovermann, K. H., and Petrie, T., An induction theorem for equivariant surgery, Am. J. Math. (I983), I369-I403. | Zbl

[DP2] Dovermann, K. H. G surgery II, Memoirs AMS 37, number 260 (May I982). | MR | Zbl

[DP3] Dovermann, K. H. Smith equivalence of representations for odd order cyclic groups, to appear in Topology. | MR | Zbl

[D] Dress, A., Induction and structure theorems for orthogonal representations of finite groups, Ann. of Math. 102 (I975), 29I-325. | MR | Zbl

[E] Ewing, J., Spheres as fixed sets, Quart. J. Math. 27 (I976), 445-455. | MR | Zbl

[H] Hirsch, M., Immersions of manifolds, Trans. AMS 93 (I959), 242-276. | MR | Zbl

[I1] Illman, S., Smooth equivariant triangulations of G manifolds for G a finite group, Math. Ann. 233 (I978), I99-220. | EuDML | MR | Zbl

[I2] Illman, S. Whitehead torsion and actions of compact Lie groups, to appear. | Zbl

[M] Milnor, J., Whitehead torsion, Bull. AMS 72 (I966), 358-426. | MR | Zbl

[O] Oliver, R., Group actions on disks, integral permutations, representations and the Burnside ring, Proc. Symp. Pure Math. AMS 32 (I978), 339-346. | MR | Zbl

[P1] Petrie, T., G surgery I-A survey, Springer Lecture Notes in Math. 664 (I978), I97-233. | MR | Zbl

[P2] Petrie, T. Three theorems in transformation groups, Springer Lecture Notes in Math. 763 (I979), 549-572. | MR | Zbl

[P3] Petrie, T. One fixed point actions on spheres II, Adv. in Math. 45 (Sept. I982), I7-70. | Zbl

[P4] Petrie, T. One fixed point actions on spheres I, Adv. in Math. 45 (Sept. I982), 3-I4. | MR | Zbl

[P6] Petrie, T., Isotropy representations of actions on disks, in preparation.

[P7] Petrie, T. Smith equivalence of representations, Proc. Cambridge Philo. Soc. 94 (I983), 6I-99. | MR | Zbl

[PR] Petrie, T., and Randall, J., Transformation groups on manifolds, Dekker Monographs Pure and Applied Math. (June I984). | Zbl

[R] Rothenberg, M., Torsion Invariants, Proc. Symp. Pure Math. AMS 32, part I (I978), 267-3II. | Zbl

[Sa] Sanchez, C., Actions of compact groups of odd order on compact orientable manifolds, Proc. AMS 54 (I976), 454-458. | MR | Zbl

[Sc1] Schultz, R., Spherelike G manifolds with exotic equivariant tangent bundles, Adv. in Math. Suppl. Studies 5 (I979), I-39. | MR | Zbl

[Sc2] Schultz, R. Differentiable group actions on homotopy spheres, Invent. Math. 31 (I975), I03-I08. | Zbl

[Sc3] Schultz, R. Differentiability and the P.A. Smith theorems for spheres, Current trends in Algebraic Topology, Canadian Math. Soc. Conf. Proc. (I982), 235-273. | Zbl

[Si] Siegel, A., Fixed point representations of group actions on spheres, Thesis, Rutgers University (I982).

[St] Stallings, J., Lectures on polyhedral topology, Tata Inst. of Fundamental Research, Bombay (I968). | Zbl

[Suh] Suh Dong, Thesis, Rutgers University (I984).

[Sm] Smith, P. A., New results and old problems in finite transformation groups, Bull. AMS 66 (I960), 40I-4I5. | MR | Zbl

[W] Wall, C. T. C., Surgery on compact manifolds, Academic Press (I970). | Zbl