Volume 3, issue 2 (2003)

Download this article
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Fixed point data of finite groups acting on 3–manifolds

Peter E Frenkel

Algebraic & Geometric Topology 3 (2003) 709–718

arXiv: math.AT/0301159


We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3–manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various non-cyclic subgroups. In Section 2, we show that all such relations are in fact equations mod 2, and we explain how the number of independent equations yields information concerning low-dimensional equivariant cobordism groups. Moreover, we restate a theorem of A Szűcs asserting that under the conditions imposed on a smooth action of G on M as above, the number of G–orbits of points x M with non-cyclic stabilizer Gx is even, and we prove the result by using arguments of G Moussong. In Sections 3 and 4, we determine all the equations for non-cyclic subgroups G of SO(3).

3–manifold, group action, fixed points, equivariant cobordism
Mathematical Subject Classification 2000
Primary: 57S17
Secondary: 57R85
Forward citations
Received: 7 January 2003
Accepted: 14 July 2003
Published: 30 July 2003
Peter E Frenkel
Department of Geometry
Mathematics Institute
Budapest University of Technology and Economics
Egry J. u. 1.
1111 Budapest