Summary: Commun. Math. Phys. 182, 303-318 (1996) Communications I
© Springer-Verlag 1996
Splitting of the Family Index
, Weiping Zhang2
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA.
Nankai Institute of Mathematics, Tianjin 300071, P.R. China.
Received: 29 January 1996/Accepted: 23 April 1996
Abstract: We establish a general splitting formula for index bundles of families of
Dirac type operators. Among the applications, our result provides a positive answer
to a question of Bismut and Cheeger [BC2].
Due to the increasing influence of the topological quantum field theory (cf. [A]),
it becomes very important to study the behavior of natural analytic invariants un-
der the splitting of manifolds. The first splitting formula, for the most fundamen-
tal invariants--the index of Dirac operators, was proved by Atiyah-Patodi-Singer