Abstract
We collect here some problems in the realm of differentiable transformation groups which have occurred to us during our collaboration in the past three years. Instead of just listing them as a sequence of questions, we try to put them together with the motivations and comments in a more organized way. It is our hope that such an effort will, indeed, make the problems more natural and inviting. We also suggest the readers to read this article together with another survey article written by the second named author for further motivation and the connections with known results (these same proceedings).
The first named author was partially supported by NSF Grant NSF GP 6520 and an Alfred P. Sloan Fellowship.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Borel, A. et. al.: Seminar on transformation groups, Annals of Math. Studies 46, Princeton University Press (1961).
Borel, A. et. al.: Le plan projectif des octaves et les spheres comme espaces homogènes, Completes Rendue de l’Academie des Sciences, Paris 230, 1378–1383 (1960).
Bredon, G.: Transformation groups on spheres with two types of orbits, Topology 3, 115–122 (1965).
Bredon, G.: Examples of differentiable group actions, Topology 3, 103–113 (1965).
Conner, P.: Retraction properties of the orbit spaces of a compact topological transformation group, Duke Math. J. 27, 341–357 (1960).
Hirzebruch, F.: Séminaire Bourbaki 1966.
Hsiang, W. C.: A note on free differentiable actions of S 1 and S 3 on homotopy spheres, Ann. of Math. 83, 266–272 (1966).
Hsiang, W. C. and W. Y. Hsiang: Classification of diiferentiable actions on S n , R n and D n with S k as the principal orbit type, Ann. of Math. 82, 421–433 (1965).
Hsiang, W. C. and W. Y. Hsiang: Differentiable Actions of compact connected classical groups I, Amer. J. Math. 89, 705–786 (1967).
Hsiang, W. C. Differentiable actions of compact connected classical groups II (in preparation).
Hsiang, W. C.: On compact subgroup of the diffeomorphism groups of Kervair spheres. Ann. of Math. 85, 359–369 (1967).
Hsiang, W. C.: Some differentiable actions of S 1 and S 3 on 11-spheres, Quarterly J. Math. (2) Oxford 15, 371–374 (1964).
Hsiang, W. C.: The degree of symmetry of homotopy spheres, to appear in Ann. of Math.
Hsiang, W. Y.: A survey article in this issue.
Hsiang, W. Y.: On the bound of the dimensions of the isometry groups of all possible riemannian metrics on an exotic sphere, Ann. of Math. 85, 351–358 (1967).
Hsiang, W. Y.: The natural metric on SO(n)/SO(n-2) is the most symmetric metric, Bull. AMS 73, 55–58 (1967).
Hsiang, W. Y., and J. C. Su: (to appear in Trans. AMS).
Jänich, K.: Differenzierbare Mannigfaltigkeiten mit Rand als Orbiträume differenzierbarer G-Mannigfaltigkeiten ohne Rand, Topology, 5, 301–320 (1966).
Montgomery, D., and C. T. Yang: The existence of slice, Ann. of Math. 65, 108–116(1957).
Montgomery, D.: Free differentiable actions on homotopy spheres, these Proceedings.
Montgomery, D. and H. Samelson: Transformation groups of spheres, Ann. of Math. 44, 454–470 (1943).
Montgomery, D., and L. Zippin: Topological transformation groups, Interscience, 1955.
Mostow, G. D.: Equivariant embedding in Euclidean space, Ann. of Math. 65, 432–446 (1957).
Palais, R.: Embedding of compact diiferentiable transformation groups in orthogonal representations, J. of Math. and Mech. 6, 673–678 (1957).
Poncet, J.: Groupes die Lie compacts de transformations de l’espace euclidean et les spheres comme espaces homogènes, Comment. Math. Helv. 33, 109–120 (1959).
Smith, P. A.: Fixed points of periodic transformations, Appendix B in Lefschetz Algebraic Topology, 1948, New York.
Wang, H. C.: Compact transformation groups of S n with an (n-1)-dimensional orbit, Amer. J. Math. 82, 698–748 (1960).
Wang, H. C.: Homogeneous spaces with non-vanishing Euler characteristics,-Ann. Math. 50, 925–953 (1949).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1968 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Hsiang, WC., Hsiang, WY. (1968). Some Problems in Differentiable Transformation Groups. In: Mostert, P.S. (eds) Proceedings of the Conference on Transformation Groups. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46141-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-46141-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46143-9
Online ISBN: 978-3-642-46141-5
eBook Packages: Springer Book Archive