1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted