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)
DOI: 10.5802/tsg.195
This electronic journal was available for many years under the link
http://www-fourier.ujf-grenoble.fr/SEMINAIRES/STSG/index.html
The link was deactivated in the early 2020s, and the article is now available under the links
https://proceedings.centre-mersenne.org/articles/10.5802/tsg.195/
http://www.numdam.org/item/?id=TSG_1997-1998__16__33_0

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