Classification of the actions of the circle on 3-manifolds

Abstract

(The manifold M6,g,h,t is an explicit sum of handles and p2 X S1's. The L'(Pt, v1)'s are lens spaces each with a specific, or standard, action. This is described more precisely in the text.) Since each allowable unordered tuple corresponds uniquely to a distinct class of equivalent actions, we can, if we are able to identify the 3-manifold, determine all the inequivalent actions on a given 3-manifold. The corollary to Theorem 4 does just this for actions with fixed points. (For example, the manifold admitting the action (0; (o, 6, 3, 5); (9, 2), (7, 5), (8, 3), (15, 6)) admits exactly 5,632 strictly inequivalent actions with fixed points and no actions without fixed points.)