Abstract
Let V be an orthogonal representation of G=S1 and let S(V), S(V⊕R) be the unit spheres in V, V⊕R respectively. In this paper we classify S1-equivariant maps S(V⊕R) → S(V). More precisely we construct an isomorphism [S(V⊕R), S(V)]G → A(V) where A(V) = = [S(V⊕R)G,S(V)G]⊕(\(\mathop \oplus \limits_H\) Z), H⊂S1 runs over all isotropy subgroups of V different from S1.
Keywords
- Homotopy Class
- Isotropy Subgroup
- Invariant Subset
- Obstruction Theory
- Representation Sphere
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G.E. Bredon. Introduction to Compact Transformation Group, Academic Press, New York and London 1972.
T. tom Dieck, Transformation Groups and Representation Theory, Lect. Notes in Math. 766, Springer, Heidelberg-New York, 1979.
G. Dylawerski, K. Gęba, J. Jodel, W. Marzantowicz, An S1-Equivariant Degree An The Fuller Index, Preprint No 64, University of Gdańsk. 1987.
R.L. Rubinsztein, On the equivariant homotopy of spheres, Dissertationes Mathematicae, No 134, Warszawa 1976.
G.B. Segal, Equivariant stable homotopy theory, Actes, Congres Inten. Math. Nice 1970, Tome 2, p. 59–63.
N. Steenrod, The topology of fibre bundles, Princeton University Press, 1951.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Dylawerski, G. (1988). An S1-degree and S1-maps between representation spheres. In: tom Dieck, T. (eds) Algebraic Topology and Transformation Groups. Lecture Notes in Mathematics, vol 1361. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083032
Download citation
DOI: https://doi.org/10.1007/BFb0083032
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50528-0
Online ISBN: 978-3-540-46036-7
eBook Packages: Springer Book Archive
