Defect of index in the theory of non-local problems and the $ \eta$-invariant
A. Yu. Savin, Boris Yu. Sternin · Sbornik Mathematics · 2004
This paper is concerned with elliptic theory on manifolds the boundary of which is a cover. Non-local boundary value problems are considered and their indices are calculated. The Atiyah-Patodi-Singer problem is studied on such manifolds. For non-trivial covers the defect of the index is calculated. The Poincare duality is constructed in -theory on the corresponding singular manifolds.