Smooth Finite Cyclic Group Actions on Positive Definite Four-Manifolds

Abstract

<p>Smooth actions of odd order cyclic groups on closed positive definite simply connected 4-manifolds are considered. For such an action, by studying its associated instanton one Yang-Mills equivariant moduli space, it is proved that the fixed point pattern of the singular set and the isotropy representations are the same as those of an equivariant connected sum of complex projective spaces acted linearly by the same group. Under certain assumptions, questions regarding the number of distinct possible isotropy representations at singular points arising in smooth actions and equivariant connected sumes of algebraic actions on 4-dimensional complex projective spaces are answered.</p>