  The Birman exact sequence describes the effect on the mapping class group of
a surface with boundary of gluing discs to the boundary components. We
construct an analogous exact sequence for the automorphism group of a free
group. For the mapping class group, the kernel of the Birman exact sequence is
a surface braid group. We prove that in the context of the automorphism group
of a free group, the natural kernel is finitely generated. However, it is not
finitely presentable; indeed, we prove that its second rational homology group
has infinite rank by constructing an explicit infinite collection of linearly
independent abelian cycles. We also determine the abelianization of our kernel
and build a simple infinite presentation for it. The key to many of our proofs
are several new generalizations of the Johnson homomorphisms.
