The Dirac Operator on Collapsing Circle Bundles
by
Bernd Ammann

The Dirac Operator on Collapsing Circle Bundles (.dvi , .ps, .ps.gz oder .pdf)
Sém. Th. Spec. Géom Inst. Fourier Grenoble 16, 33-42 (1998)

Abstract

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.

Mathematics Subject Classification

58G25, 58G30, 53C25

Keywords

Dirac operator, circle bundles, collapse, convergence of eigenvalues, projectable spin structures
Bernd Ammann, 19.10.1998