Spherical isotropy representations

Ted Petrie; John Randall

Publications Mathématiques de l'IHÉS (1985)

  • Volume: 62, page 5-40
  • ISSN: 0073-8301

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Petrie, Ted, and Randall, John. "Spherical isotropy representations." Publications Mathématiques de l'IHÉS 62 (1985): 5-40. <http://eudml.org/doc/104009>.

@article{Petrie1985,
author = {Petrie, Ted, Randall, John},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {finite group actions on homotopy spheres; Smith equivalent fixed; points},
language = {eng},
pages = {5-40},
publisher = {Institut des Hautes Études Scientifiques},
title = {Spherical isotropy representations},
url = {http://eudml.org/doc/104009},
volume = {62},
year = {1985},
}

TY - JOUR
AU - Petrie, Ted
AU - Randall, John
TI - Spherical isotropy representations
JO - Publications Mathématiques de l'IHÉS
PY - 1985
PB - Institut des Hautes Études Scientifiques
VL - 62
SP - 5
EP - 40
LA - eng
KW - finite group actions on homotopy spheres; Smith equivalent fixed; points
UR - http://eudml.org/doc/104009
ER -

References

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  1. [A1] ATIYAH, M. F., Characters and cohomology, Inst. Hautes Etudes Sci. Publ. Math. No. 9 (I96I), 23-64. MR26 #6228
  2. [AB] ATIYAH, M. F. and BOTT, R., The Lefschetz fixed point theorem for Elliptic complexes II, Ann. of Math. 86 (I967), 45I-49I. 
  3. [AS] ATIYAH, M. F. and SEGAL, G., Equivariant K-theory and completion, J. Diff. Geometry 3 (I969), I-I8. Zbl0215.24403MR41 #4575
  4. [B1] BREDON, G., Representations at fixed points of smooth actions of compact groups, Ann. of Math. 89 (I969), 5I5-532. Zbl0162.27404MR39 #7628
  5. [B2] BREDON, G.Introduction to transformation groups, Academic Press (I972). 
  6. [CS] CAPPELL, S., and SHANESON, J., Fixed points of periodic differentiable maps, Invent. Math. 68 (I982), I-I9. Zbl0507.57027MR84a:57038
  7. [C] CHO, Eung, Thesis, Rutgers University (I984). 
  8. [Dov] DOVERMANN, K. H., Even dimensional Smith equivalent representations, Algebraic Topology Conf. Aarhus, Springer Lecture Notes in Math. 1051 (I982), 587-602. Zbl0543.57027MR86a:57034
  9. [DP1] DOVERMANN, K. H., and PETRIE, T., An induction theorem for equivariant surgery, Am. J. Math. (I983), I369-I403. Zbl0535.57020
  10. [DP2] DOVERMANN, K. H.G surgery II, Memoirs AMS 37, number 260 (May I982). Zbl0495.57014MR84c:57025
  11. [DP3] DOVERMANN, K. H.Smith equivalence of representations for odd order cyclic groups, to appear in Topology. Zbl0597.57014
  12. [D] DRESS, A., Induction and structure theorems for orthogonal representations of finite groups, Ann. of Math. 102 (I975), 29I-325. Zbl0315.20007MR52 #8235
  13. [E] EWING, J., Spheres as fixed sets, Quart. J. Math. 27 (I976), 445-455. Zbl0342.55013MR55 #4234
  14. [H] HIRSCH, M., Immersions of manifolds, Trans. AMS 93 (I959), 242-276. Zbl0113.17202MR22 #9980
  15. [I1] ILLMAN, S., Smooth equivariant triangulations of G manifolds for G a finite group, Math. Ann. 233 (I978), I99-220. Zbl0359.57001MR58 #18474
  16. [I2] ILLMAN, S.Whitehead torsion and actions of compact Lie groups, to appear. Zbl0563.57016
  17. [M] MILNOR, J., Whitehead torsion, Bull. AMS 72 (I966), 358-426. Zbl0147.23104MR33 #4922
  18. [O] OLIVER, R., Group actions on disks, integral permutations, representations and the Burnside ring, Proc. Symp. Pure Math. AMS 32 (I978), 339-346. Zbl0455.57020
  19. [P1] PETRIE, T., G surgery I-A survey, Springer Lecture Notes in Math. 664 (I978), I97-233. Zbl0403.57003MR80g:57049
  20. [P2] PETRIE, T.Three theorems in transformation groups, Springer Lecture Notes in Math. 763 (I979), 549-572. Zbl0419.57011MR82b:57031
  21. [P3] PETRIE, T.One fixed point actions on spheres II, Adv. in Math. 45 (Sept. I982), I7-70. Zbl0502.57021
  22. [P4] PETRIE, T.One fixed point actions on spheres I, Adv. in Math. 45 (Sept. I982), 3-I4. Zbl0502.57021
  23. [P6] PETRIE, T., Isotropy representations of actions on disks, in preparation. 
  24. [P7] PETRIE, T.Smith equivalence of representations, Proc. Cambridge Philo. Soc. 94 (I983), 6I-99. Zbl0526.57026MR85i:57011
  25. [PR] PETRIE, T., and RANDALL, J., Transformation groups on manifolds, Dekker Monographs Pure and Applied Math. (June I984). Zbl0574.57001
  26. [R] ROTHENBERG, M., Torsion Invariants, Proc. Symp. Pure Math. AMS 32, part I (I978), 267-3II. Zbl0426.57013
  27. [Sa] SANCHEZ, C., Actions of compact groups of odd order on compact orientable manifolds, Proc. AMS 54 (I976), 454-458. Zbl0316.57022MR53 #11641
  28. [Sc1] SCHULTZ, R., Spherelike G manifolds with exotic equivariant tangent bundles, Adv. in Math. Suppl. Studies 5 (I979), I-39. Zbl0453.57028MR80h:57046
  29. [Sc2] SCHULTZ, R.Differentiable group actions on homotopy spheres, Invent. Math. 31 (I975), I03-I08. Zbl0335.57025
  30. [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. Zbl0566.57019
  31. [Si] SIEGEL, A., Fixed point representations of group actions on spheres, Thesis, Rutgers University (I982). 
  32. [St] STALLINGS, J., Lectures on polyhedral topology, Tata Inst. of Fundamental Research, Bombay (I968). Zbl0182.26203
  33. [Suh] SUH DONG, Thesis, Rutgers University (I984). 
  34. [Sm] SMITH, P. A., New results and old problems in finite transformation groups, Bull. AMS 66 (I960), 40I-4I5. Zbl0096.37501MR23 #A2880
  35. [W] WALL, C. T. C., Surgery on compact manifolds, Academic Press (I970). 

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