References
Alexander, J. P., Hamrick, G. C., Vick, J. W.: Involutions on homotopy spheres. Invent. Math.24, 35–50 (1974)
Anderson, D. W., Brown, E. H., Peterson, F.: The structure of the spin cobordism ring. Ann. Math.86, 271–298 (1967)
Becker, J. C., Schultz, R. E.: Equivariant function spaces and stable homotopy theory I. Comment. Math. Helv.49, 1–34 (1974)
Boardman, J. M., Vogt, R. M.: Homotopy invariant algebraic structures on topological spaces. Lecture Notes in Math.347. Berlin-Heidelberg-New York: Springer 1973
Bredon, G.: Aπ * structure forΘ * and applications to transformation groups. Ann. Math.86, 434–448 (1967)
Bredon, G.: Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46. New York: Academic Press 1972
Bredon, G.: Classification of regular actions of classical groups with three orbit types, mimeographed, Rutgers University, 1973 (Revised edition to appear in Ann. of Math. Studies)
Browder, W.: Surgery and the theory of differentiable transformation groups. Proceedings of the conference on transformation groups (New Orleans, 1967), pp. 1–46. New York: Springer 1968
Browder, W.: Surgery on simply connected manifolds. In: Ergebnisse der Mathematik, Bd. 65. New York: Springer 1972
Browder, W., Petrie, T.: Semifree and quasifreeS 1 actions on homotopy spheres. Essays on topology and related topics (Memoires dediés à G. de Rham), pp. 136–146. New York: Springer 1970
Browder, W., Petrie, T.: Diffeomorphisms of manifolds and semifree actions on homotopy spheres. Bull. Amer. Math. Soc.77, 160–163 (1971)
Brumfiel, G.: On the homotopy groups of BPL and PL/0-I. Ann. Math.87, 291–311 (1968)
Brumfiel, G.: DifferentiableS 1 actions on homotopy spheres, mimeographed. Berkeley: University of California 1969
Cappell, S.: Uhitary nilpotent groups and HermitianK-theory I. Bull. Amer. Math. Soc.80, 1117–1122 (1974)
Cappell, S., Shaneson, J.: The codimension two placement problem and homology equivalent manifolds. Ann. Math.99, 277–348 (1974)
Connolly, F.: Linking numbers and surgery. Topology12, 389–410 (1973)
Davis, M., Hsiang, W.-C., Hsiang, W.-Y.: to appear
Dold, A., Lashof, R.: Principal quasifibration and fibre homotopy equivalence of bundles. Illinois J. Math.3, 285–305 (1959)
Douady, A., Hérault, L.: Arrondisement des variétès à coins (appendix to a paper by A. Borel and J.-P. Serre). Comment. Math. Helv.48, 484–489 (1973)
Friedlander, E. M.: The etale homotopy theory of a geometric fibration. Manuscripta Math.10, 209–244 (1973)
Hirzebruch, F., Mayer, K.:O(n)-Mannigfaltigkeiten, Exotische Sphären, und Singularitäten. Lecture Notes in Math.57. New York: Springer 1968
Holzsager, R.: Stable splitting ofK(G, 1). Proc. Amer. Math. Soc.31, 305–306 (1972)
Hsiang, W.-C., Hsiang, W.-Y: Differentiable actions of compact connected classical groups I. Amer. J. Math.89, 705–786 (1967);ibid. Hsiang, W.-C., Hsiang, W.-Y: Differentiable actions of compact connected classical groups II. Ann. Math.92, 189–223 (1970)
Hsiang, W.-C., Hsiang, W.-Y.: The degree of symmetry of homotopy spheres. Ann. Math.89, 52–67 (1969)
Hsiang, W.-Y.: On the unknottedness of the fixed point set of differentiable circle group actions on spheres—P. A. Smith conjecture. Bull. Amer. Math. Soc.70, 678–680 (1964)
Hsiang, W.-Y.: On the degree of symmetry and the structure of highly symmetric manifolds. Tamkang J. Math.2, 1–22 (1971)
Jones, L.: The converse to the fixed point theorem of P. A. Smith: I. Ann. Math.94, 52–68 (1971)
Jones, L.:Ibid.. Indiana University Math. J.22, 309–325 (1972); correction24, 1001–1003 (1975)
Jones, L.: Patch spaces. Ann. Math.97, 306–343 (1973); correction102. 183–185 (1975)
Kervaire, M., Milnor, J.: Groups of homotopy spheres. Ann. Math.78, 514–537 (1963)
Lawson, H. B., Yau, S.-T.: Scalar curvature, nonabelian group actions, and the degree of symmetry of exotic spheres. Comment. Math. Helv.49, 232–244 (1974)
Lee, R.: Nonexistence of free differentiable actions ofS 1 and ℤ2 on homotopy spheres. Proceedings of the Conference on Transformation Groups (New Orleans, 1967), pp. 208–209. New York: Springer 1968
Levine, J.: A classification of differentiable knots. Ann. Math.82, 15–50 (1965)
Levine, J.: Self-equivalences ofS n×S k. Trans. Amer. Math. Soc.143, 523–543 (1969)
Levine, J.: Semi-free circle actions on spheres. Invent. math.22, 161–186 (1973)
Lynch, P.: FramedG-homology spheres, Ph. D. Thesis, Brandeis University, 1971
Milnor, J.: Remarks concerning spin manifolds, differential and combinatorial topology (A symposium in honor of M. Morse), Princeton Mathematical Series No. 27, 55–62. Princeton: Princeton University Press 1965
Mosher, R., Tangora, M.: Cohomology operations and applications in homotopy theory. New York: Harper and Row 1968
Rothenberg, M.: Differentiable group actions on spheres. Proceedings of the advanced study institute on algebraic topology (Aarhus, 1970), 455–475. Mathematical Institute, Aarhus University, Aarhus, 1970
Rothenberg, M., Sondow, J.: Nonlinear smooth representations of compact Lie groups. Mimeographed, University of Chicago, 1969
Rourke, C. P.: The Hauptvermuting according to Sullivan. Mimeographed, Institute for Advanced Study, 1968
Schultz, R.: The nonexistence of freeS 1 actions on some homotopy spheres. Proc. Amer. Math. Soc.27, 595–597 (1971)
Schultz, R.: Improved estimates for the degree of symmetry of certain homotopy spheres. Topology10, 227–235 (1971)
Schultz, R.: Semifree circle actions and the degree of symmetry of homotopy spheres. Amer. J. Math.93, 829–839 (1971)
Schultz, R.: Composition constructions on diffeomorphisms ofS p×S q. Pacific J. Math.42, 739–754 (1972)
Schultz, R.: Circle actions on homotopy spheres bounding plumbing manifolds. Proc. Amer. Math. Soc.36, 297–300 (1972)
Schultz, R.: Circle actions on homotopy spheres bounding generalized plumbing manifolds. Math. Ann.205, 201–210 (1973)
Schultz, R.: Homotopy sphere pairs admitting semifree differentiable actions. Amer. J. Math.96, 308–323 (1974)
Schultz, R.: Differentiable ℤ p actions on homotopy spheres. Bull. Amer. Math. Soc.80, 961–964 (1974)
Schultz, R.: Circle actions on homotopy spheres not bounding spin manifolds. Trans. Amer. Math. Soc. to appear
Steenrod, N., Epstein, D. B. A.: Cohomology operations. Annals of mathematics studies No. 50. Princeton: Princeton University Press 1962
Sullivan, D.: Triangulating homotopy equivalences, Ph.D. Thesis, Princeton University, 1965
Sullivan, D.: Smoothing homotopy equivalences. Mimeographed, University of Warwick, 1966
Sullivan, D.: Geometric topology I. Localization, periodicity, and Galois symmetry. Mimeographed, M.I.T., 1970
Sullivan, D.: Genetics of homotopy theory and the Adams conjecture. Ann. Math.100, 1–79 (1974)
Toda, H.:p-primary components of homotopy groups IV. Compositions and toric constructions. Mem. College Sci. Kyoto University32, 297–332 (1959)
Toda H.: Composition methods in homotopy groups of spheres. Ann. of Math. Studies No. 49. Princeton: Princeton University Press 1962
Wall, C. T. C.: Surgery on compact manifolds. London Mathematical Society Monographs No. 1. New York: Academic Press 1970
Schultz, R.: Homotopy decompositions of equivariant function spaces I. Spaces of principal bundle maps. Math. Z.131, 49–75 (1973)
Quinn, F.: Semifree group actions and surgery onPL homology manifolds. Geometric Topology (Proceedings of the Geometric Topology Conference, Park City, Utah, 1974). Lecture Notes in Math.438, 395–414. Berlin, Heidelberg, New York: Springer 1975
Author information
Authors and Affiliations
Additional information
Partially supported by NSF Grants GP-19530A1/A2, GP-36418X, and MPS74-03609.
Rights and permissions
About this article
Cite this article
Schultz, R. Differentiable group actions on homotopy spheres. Invent Math 31, 105–128 (1976). https://doi.org/10.1007/BF01404111
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01404111