ETA-INVARIANTS AND DETERMINANT LINES

Authors
DAI XZ FREED DS
Citation
Xz. Dai et Ds. Freed, ETA-INVARIANTS AND DETERMINANT LINES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 320(5), 1995, pp. 585-591
Citations number
19
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
320
Issue
5
Year of publication
1995
Pages
585 - 591
Database
ISI
SICI code
0764-4442(1995)320:5<585:EADL>2.0.ZU;2-M
Abstract
We investigate the eta-invariant of an odd dimensional manifold with b oundary. The exponential of the eta-invariant lives in the determinant line of the boundary. Our main results are a variational formula and a gluing law for this relative invariant. We apply these results to re prove the formulae for the curvature and the holonomy of the natural c onnection on the determinant line bundle of a family of Diract operato rs.