 
Summary: January 25, 2006 13:32 Proceedings Trim Size: 9in x 6in Dai
Analysis, Geometry and Topology
of Elliptic Operators, 153185
c 2006 World Scientific
ETA INVARIANTS FOR MANIFOLD WITH BOUNDARY
XIANZHE DAI
Math. Dept., UCSB,
Santa Barbara, CA 93106, USA
dai@math.ucsb.edu
Dedicated to Krzysztof P. Wojciechowski on his 50th birthday
For a compact manifold with boundary, M, there are well known local boundary
conditions that make the de Rham operator A = d+ elliptic, namely the absolute
and relative boundary conditions. We study the eta invariants of such elliptic
boundary value problems under the metric deformation
g =
dx2
x2 + 2
+ g,
where x C(M) is, near the boundary, the geodesic distance to the boundary,
and g is a Riemannian metric on M which is of product type near the boundary.
