Kp. Wojciechowski, THE ADDITIVITY OF THE ETA-INVARIANT - THE CASE OF A SINGULAR TANGENTIAL OPERATOR, Communications in Mathematical Physics, 169(2), 1995, pp. 315-327
We prove the decomposition formula for the eta-invariant of the compat
ible Dirac operator on a closed manifold M which is a sum of two subma
nifolds with common boundary.