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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 354, Number 1, Pages 107122
S 0002-9947(01)02863-X
Article electronically published on August 20, 2001
APS BOUNDARY CONDITIONS, ETA INVARIANTS AND
ADIABATIC LIMITS
XIANZHE DAI
Abstract. We prove an adiabatic limit formula for the eta invariant of a
manifold with boundary. The eta invariant is defined using the Atiyah-Patodi-
Singer boundary condition and the underlying manifold is fibered over a man-
ifold with boundary. Our result extends the work of Bismut-Cheeger to man-
ifolds with boundary.
1. Introduction
The -invariant, introduced by Atiyah-Patodi-Singer in their seminal work [APS],
is the correction term (from the boundary) for the index formula on a manifold with
boundary. The adiabatic limit refers to the geometric degeneration in which the
metric is been blown up along certain directions. The study of the adiabatic limit
of the -invariant is initiated by E. Witten [W], who relates the adiabatic limit of
the -invariant to the holonomy of determinant line bundle, the so-called "global

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics