The Dirac Operator on Collapsing Circle Bundles
by
Bernd Ammann
The Dirac Operator on Collapsing Circle Bundles
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Sém. Th. Spec. Géom Inst. Fourier Grenoble
16, 33-42
(1998)
We study the behavior of the spectrum of the Dirac operator
on collapsing $S^1$-bundles. Convergent eigenvalues will
exist if and only if the spin structure is projectable.
This paper generalizes the collapse results of a
previous paper
(collaboration with
Christian Bär)
to the case of non-geodesic
fibers.
58G25, 58G30, 53C25
Keywords
Dirac operator, circle bundles,
collapse, convergence of eigenvalues, projectable spin structures
Bernd Ammann, 19.10.1998