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-invariant and flat vector bundles
We present an alternate definition of the mod {\bf Z} component of the
Atiyah-Patodi-Singer invariant associated to (not necessary unitary)
flat vector bundles, which identifies explicitly its real and imaginary parts.
This is done by combining a deformation of flat connections introduced in a
previous paper with the analytic continuation procedure appearing in the
original article of Atiyah, Patodi and Singer.Comment: 6 page
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