Editing Holonomy (section)

===Monodromy===
The holonomy bundle ''H''(''p'') is a principal bundle for <math>\operatorname{Hol}_p(\omega),</math> and so also admits an action of the restricted holonomy group <math>\operatorname{Hol}^0_p(\omega)</math> (which is a normal subgroup of the full holonomy group). The discrete group <math>\operatorname{Hol}_p(\omega)/\operatorname{Hol}^0_p(\omega)</math> is called the [[monodromy group]] of the connection; it acts on the quotient bundle <math>H(p)/ \operatorname{Hol}^0_p(\omega).</math> There is a surjective homomorphism <math>\varphi: \pi_1 \to \operatorname{Hol}_p(\omega)/\operatorname{Hol}^0_p(\omega),</math> so that <math>\varphi\left(\pi_1(M)\right)</math> acts on <math>H(p)/ \operatorname{Hol}^0_p(\omega).</math> This action of the fundamental group is a '''monodromy representation''' of the fundamental group.<ref>{{harvnb|Sharpe|1997|loc=§3.7}}</ref>