Semifree actions on spheres

The article presents the main results concerning smooth semifree actions of finite groups on spheres. One shows that for every holomorphic function having an isolated singularity, there exists a smooth semifree action on a (possibly homotopic) sphere where the fixed-point set is the boundary for the singularity of the given function. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 197–207, 2005.