A topological defect separating a pair of two-dimensional CFTs is a
codimension one interface along which all components of the stress-energy
tensor glue continuously. We study topological defects of the bosonic, (0,1)-
and (0,2)-supersymmetric sigma models in two dimensions. We find a geometric
classification of such defects closely analogous to that of A-branes of
symplectic manifolds, with the role of symplectic form played instead by a
neutral signature metric. Alternatively, we find a compact description in terms
of a generalized metric on the product of the targets. In the (0,1) case, we
describe the target space geometry of a bundle in which the fermions along the
defect take values. In the (0,2) case, we describe the defects as being
simultaneously A-branes and B-branes.Comment: 21 pages, late
