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

First of all this is my first post and it's in regards to something I am (supposed to be) learning for my research. The topic is Algebraic Topology, so this was the closest general topic I could find.

The question is in regards to the connection between covering spaces and the fundamental group. I had a conversation with my advisor about CP_2 (complex projective plane in 2 D), and she said "Since CP_2 is simply connected, there cannot be any actual finite covering because these would correspond to normal subgroups of the fundemental group". Then she goes on to talk about branched coverings. Now, I understand that simple connectivity implies the fundamental group is trivial, and that a covering space p:X'->X means p(pi(X'))->pi(X) must be injective, but I don't really understand her "finiteness" remark. Does anyone have any thoughts on this?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple connectivity and finite coverings

Loading...

Similar Threads for Simple connectivity finite |
---|

A Connection 1-forms to Christoffel symbols |

I Connections on principal bundles |

A Is the Berry connection a Levi-Civita connection? |

A Can you give an example of a non-Levi Civita connection? |

A Simple metric tensor question |

**Physics Forums | Science Articles, Homework Help, Discussion**