1211.4044 (Klaus Kirsten et al.)

Analytic surgery of the zeta function    [PDF]

Klaus Kirsten, Paul Loya

In this paper we study the asymptotic behavior (in the sense of meromorphic functions) of the zeta function of a Laplace-type operator on a closed manifold when the underlying manifold is stretched in the direction normal to a dividing hypersurface, separating the manifold into two manifolds with infinite cylindrical ends. We also study the related problem on a manifold with boundary as the manifold is stretched in the direction normal to its boundary, forming a manifold with an infinite cylindrical end. Such singular deformations fall under the category of "analytic surgery", developed originally by Hassell, Mazzeo and Melrose \cite{mazz95-5-14,hass95-3-115,hass98-6-255} in the context of eta invariants and determinants.

View original: http://arxiv.org/abs/1211.4044