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**shoplifter** View $\displaystyle S^3$ as the unit sphere in $\displaystyle \mathbb{C}^2$. Now,

1. What are the path connected components of the subset of $\displaystyle S^3$ described by the equation $\displaystyle x^3 + y^6 = 0$, where the x and y refer to the coordinates (in $\displaystyle \mathbb{C}$)?

2. Is it true that the similar subset $\displaystyle x^2 + y^5 = 0$ is homeomorphic to the circle?

3. what is the fundamental group of $\displaystyle S^3 - K$, where K is the subset in the 2nd part of the problem?

thnx