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2003 Fixed point data of finite groups acting on 3–manifolds
Peter E Frenkel
Algebr. Geom. Topol. 3(2): 709-718 (2003). DOI: 10.2140/agt.2003.3.709


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 xM 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).


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Peter E Frenkel. "Fixed point data of finite groups acting on 3–manifolds." Algebr. Geom. Topol. 3 (2) 709 - 718, 2003.


Received: 7 January 2003; Accepted: 14 July 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1034.57015
MathSciNet: MR1997335
Digital Object Identifier: 10.2140/agt.2003.3.709

Primary: 57S17
Secondary: 57R85

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.3 • No. 2 • 2003
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