Iterated monodromy group
The notion of iterated monodromy group is defined in the context of a covering map from a subspace of a space to the whole space (the covering map obviously differs from the inclusion of the subspace). The key word here is iterated -- the fact that the cover itself can also be identified as a subset of the space allows us to consider iterating the function used for the covering map.
- is the fundamental group of at basepoint .
- represents the homomorphism from to viewed in the context of the covering map . Note that in the case , we get the usual monodromy action for and the quotient by the kernel is the usual monodromy group.
In other words, the iterated monodromy group stores the fundamental group modulo those loops that act trivially on all sets.