  We introduce a small slit into a planar domain and study the resulting effect
upon the eigenvalues of the Laplacian. In particular, we show that as the
length of the slit tends to zero, each real-analytic eigenvalue branch tends to
an eigenvalue of the original domain. By combining this with our earlier work
(arXiv:math/0703616), we obtain the following application: The generic multiply
connected polygon has simple spectrum.
