(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Fundamental groups of subsets of S^3

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