Superposition Principle for the Relative Index

Abstract

The superposition principle outlined in the introduction deals with modifications (surgeries) of elliptic operators performed on two disjoint closed subsets, say A and B, of the manifold M on which these operators are defined and says that the index increments ∆_A and ∆_B resulting from these surgeries are independent (i.e., are just summed if both surgeries are carried out simultaneously).