Title: Index Theorem for Projective Families

Abstract: I will talk about projective families index theory, initially done in collaboration with Isadore Singer and with Richard Melrose. It generalises the Atiyah-Singer index theorem which has a myriad of applications. The recent result uses “small” bundle gerbes, and I will discuss the existence of small bundle gerbes, especially on 3-manifolds. This most recent theorem is work in progress with Richard Melrose.

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