When D-branes Break

We analyze the possible configurations of D-branes breaking on other D-branes. We describe these configurations in the context of a brane-antibrane effective theory in two ways. First as a tachyon configuration representing a non-trivial bundle over the sphere surrounding the end of the brane a la Polchinski, and second in terms of tachyon solitons using homotopy theory. Surprisingly, in some cases there are topologically stable configurations of broken branes.