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Fundamental groups of subsets of S^3

  1. May 5, 2010 #1
    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.
  2. jcsd
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