The Dirac Operator on Hyperbolic Manifolds of Finite Volume

Details The Dirac Operator on Hyperbolic Manifolds of Finite Volume The Dirac Operator on Hyperbolic Manifolds of Finite Volume

2000-10-25

arxiv.org/abs/math/0010233v1

J. Diff. Geom. 54, 439-488 (2000)

Mathematics

Differential Geometry

Latex, 43 pages, 9 figures, uses bbold.sty (included) and pstricks macro package; to appear in J. Diff. Geom

Scientific paper

We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking numbers for when essential spectrum can occur. We compute the accumulation rate of the eigenvalues of a sequence of closed hyperbolic 2- or 3-manifolds degenerating into a noncompact hyperbolic manifold of finite volume. It turns out that in three dimensions there is no clustering at all.

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