Hi!(adsbygoogle = window.adsbygoogle || []).push({});

Suppose we have a topological space [itex]X[/itex], a point [itex]x\in X[/itex] and a homomorphism [itex]\rho:\pi(X,x) \rightarrow S_n[/itex] with transitive image. Consider the subgroup [itex]H[/itex] of [itex]\pi(X,x)[/itex] consisting of those homotopy classes [itex][\gamma][/itex] such that [itex]\rho([\gamma])[/itex] fixes the index [itex]1\in \{1,\ldots,n\}[/itex]. I know that [itex]H[/itex] induces a covering space [itex]p:Y\rightarrow X[/itex]. However, I can't understand why the monodromy map of [itex]p[/itex] is exactly [itex]\rho[/itex].

Can anyone help me?

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

Join Physics Forums Today!

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

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

# Monodromy map

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