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 .
"Fixed point data of finite groups acting on 3–manifolds." Algebr. Geom. Topol. 3 (2) 709 - 718, 2003. https://doi.org/10.2140/agt.2003.3.709