Hurewicz theorem

Overview

The Hurewicz theorem gives a relationship between homotopy group and homology groups.

$n=1$ case

For the case where $n=1$, we are looking at the fundamental group and its relationship to the first singular homology group $H_1(X)$.

Statement

$H_1(X)\stackrel{\sim }{\to }{\pi }_1(X{)}_{ab}$

Proof

todo