- #1

PsychonautQQ

- 784

- 10

## Homework Statement

Let p: E-->B be a covering map, let p(e_0)=b_0 and let E be path connected. Show that there is a bijection between the collection of right cosets of p*F(E,e_0) in F(B,b_0) (where p* is the homomorphism of fundamental groups induced by p and F(E,e_0),F(B,b_0) are the fundamental groups of E and B based at e_0 and b_0 respectively) and the preimage of b_0 under the covering map p.

## Homework Equations

## The Attempt at a Solution

I have already showed that the homomorphism induced by p injects F(E,e_0) into F(B,e_0). Now I'm trying to show why the cosets defined above have a bijective correspondence to the preimage of the covering map of b_0... E being path connected definitely has something to do with it. Does anyone have any good hints/tips/insights? I seem to be going in circles >.<