Glueing at infinity and invariance of the spectrum of the Laplacian

Abstract

On this poster we introduce the technique of glueing two hyperbolic manifolds $M_{1}$ and $M_2$ along a geodesic at infinity. We then compare the spectral theory of the obtained glued manifold with the spectral theory of the disjoint union of $M_1$ and $M_2$. Our main result shows that these spectral theories do in fact coincide.