Analytic Surgery of the Zeta Function

作者：Kirsten Klaus^*; Loya Paul

来源：Communications in Mathematical Physics, 2012, 310(1): 181-215.

DOI：10.1007/s00220-011-1412-9

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 %26quot;analytic surgery%26quot;, developed originally by Hassell (Comm Anal Geom 6:255-289, 1998), Hassell et al. (Comm Anal Geom 3:115-222, 1995) and Mazzeo and Melrose (Geom Funct Anal 5:14-75, 1995) in the context of eta invariants and determinants.

• 出版日期2012-2