I was wondering if there is a description of the mapping class group of a wedge of $n$ circles.
Are the only kinds of homeomorphism classes in the mapping glass group are compositions of permutations of the circles and maps which send a circle to its inverse?
What about maps which send a circle from the wedge to a multiple of another circle? By multiple, I mean concatenating a circle several times.
Or maps that send a circle to two other circles concatenated?