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

The eigenvalues of the Laplacian on domains with small slits