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Abstract
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We consider fully effective orientation-preserving smooth actions of a given finite group
on smooth, closed,
oriented 3–manifolds .
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
on
as above, the
number of –orbits
of points with
non-cyclic stabilizer
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
of
.
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Keywords
3–manifold, group action, fixed points, equivariant
cobordism
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Mathematical Subject Classification 2000
Primary: 57S17
Secondary: 57R85
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Publication
Received: 7 January 2003
Accepted: 14 July 2003
Published: 30 July 2003
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