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

  1. Mar 17, 2010 #1
    I need to calculate the fundamental group of the following spaces:

    [itex] X_1 = \{ (x,y,z) \in \mathbb{R}^3 | x>0 \}[/itex]
    [itex] X_2 = \{ (x,y,z) \in \mathbb{R}^3 | x \neq 0 \}[/itex]
    [itex] X_3 = \{ (x,y,z) \in \mathbb{R}^3 | (x,y,z) \neq (0,0,0) \}[/itex]
    [itex] X_4 = \mathbb{R}^3 \backslash \{ (x,y,z) \in \mathbb{R}^3 | x=0,y=0, 0 \leqslant z \leqslant 1 \} [/itex]
    [itex] X_5 = \mathbb{R}^3 \backslash \{ (x,y,z) \in \mathbb{R}^3 | x=0, 0 \leqslant y \leqslant 1 \} [/itex]

    I fundamentally do not understand what a fundamental group is of how to calculate it. I have read the notes on this but they are so so abstract.
  2. jcsd
  3. Mar 17, 2010 #2
    What is the definition of a fundamental group?
  4. Mar 17, 2010 #3
    ok. i think i have answers for the first 3 that im happy with (ive discussed this with a coursemate)

    the 4th one i believe the fundamental group is trivial as any path can be contracted to a point. is this correct?

    and the 5th one is R£ with a "sheet" removed is was going to say that we can pull the space in around the sheet making a rectangle taht can then be deformed into a circle. this means the fundamental group of X5 is isomoprhic to that of S1 i.e. it is [itex]\mathbb{Z}[/itex]. is this correct?

  5. Mar 17, 2010 #4

    thanks. could you take a look at my above post please?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook