On the intersection forms of spin 4–manifolds bounded by spherical 3–manifolds

Abstract

We determine the contributions of isolated singularities of spin $V$ 4–manifolds to the index of the Dirac operator over them. From these data we derive certain constraints on the intersection forms of spin 4–manifolds bounded by spherical 3–manifolds, and also on the embeddings of the real projective planes into 4–manifolds.