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David White
David White
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It is well knowknown that the fundamental group of a path connected-connected topological group is abelian. Suppose that $G$ is a connected topological group and let $Ab(G)$ the abelianization of the topological group $G$. Is there a relation between $\pi_{1}G$ and $\pi_{1}(Ab(G))$ ?

It is well know that the fundamental group of a path connected topological group is abelian. Suppose that $G$ is a connected topological group and let $Ab(G)$ the abelianization of the topological group $G$. Is there a relation between $\pi_{1}G$ and $\pi_{1}(Ab(G))$ ?

It is well known that the fundamental group of a path-connected topological group is abelian. Suppose that $G$ is a connected topological group and let $Ab(G)$ the abelianization of the topological group $G$. Is there a relation between $\pi_{1}G$ and $\pi_{1}(Ab(G))$ ?

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lab
lab
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Fundamental group of a topological group

It is well know that the fundamental group of a path connected topological group is abelian. Suppose that $G$ is a connected topological group and let $Ab(G)$ the abelianization of the topological group $G$. Is there a relation between $\pi_{1}G$ and $\pi_{1}(Ab(G))$ ?