Cusp geometry and the cobordism invariance of the index
Abstract
Description
The cobordism invariance of the index on closed manifolds is reproved using the calculus of cusp pseudodifferential operators on a manifold with boundary. More generally, on a compact manifold with corners, the existence of a symmetric cusp differential operator of order 1 and of Dirac type near the boundary implies that the sum of the indices of the induced operators on the hyperfaces is null.
17 pages, abridged version, to appear in Adv. Math
17 pages, abridged version, to appear in Adv. Math