1. The problem statement, all variables and given/known data View S^3 as the unit sphere in C^2. Now, 1. What are the path connected components of the subset of S^3 described by the equation x^3 + y^6 = 0, where the x and y refer to the coordinates (in C)? 2. Is it true that the similar subset x^2 + y^5 = 0 is homeomorphic to the circle? 3. what is the fundamental group of S^3 - K, where K is the subset in the 2nd part of the problem? 2. Relevant equations we may (and i assume we have to) use van kampen's theorem at some point. 3. The attempt at a solution i really can't get started. can't think of any theorem (and i combed munkres's book) involving path connected components based on subsets determined by an equation -- any help or hint will be appreciated a lot. thnx.