Vol. 84, No. 2, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Nonlinear smooth representations of compact Lie groups

Melvin Gordon Rothenberg and Jonathan David Sondow

Vol. 84 (1979), No. 2, 427–444
Abstract

We study semi-free (= free off the fixed-point set) smooth actions of a compact Lie group G on disks and spheres with fixed-point set a disk or sphere, respectively. In dimensions 6 and codimension 2 we obtain a complete classification for such actions on disks and a partial classification for spheres, together with partial results in dimension 5 or codimension 2. We show that semi-free smooth actions of G on the n-disk Dn, n 6 + dimG, with fixed-point set an (n-k)-disk, k2, are classified by two invariants:

  1. a free orthogonal action of G on the (k-1)-sphere Sk1 (the representation at the fixed points) and
  2. an element of the Whitehead group Wh(πo(G)).

Mathematical Subject Classification 2000
Primary: 57S15
Milestones
Received: 10 February 1978
Published: 1 October 1979
Authors
Melvin Gordon Rothenberg
Jonathan David Sondow