Topology of strongly polar weighted homogeneous links

Abstract

We consider a canonical $S^1$ action on $S^3$ which is defined by $(\rho ,(z_1,z_2))\mapsto (z_1{\rho }^p,z_2{\rho }^q)$ for $\rho \in S^1$ and $(z_1,z_2)\in S^3\subset {\mathbb{C}}^2$. We consider a link consisting of finite orbits of this action, which some of the orbits are reversely oriented. Such a link appears as a link of a certain type of mixed polynomials. We study the space of such links and show smooth degeneration relations.