Algebraic & Geometric Topology

Fixed point data of nite groups acting on 3{manifolds Peter E. Frenkel Abstract We consider fully eective orientation-preserving smooth ac-tions of a given nite group G on smooth, closed, oriented 3{manifolds M. We investigate the relations that necessarily hold between the numbers of xed 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 num-ber of independent equations yields information concerning low-dimensional equivariant cobordism groups. Moreover, we restate a theorem of A. Sz}ucs asserting that under the conditions imposed on a smooth action of G on M as above, the number of G-orbits of points x 2M 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 subgroup