Title: Signature Theorem for Manifolds with Boundary Abstract: The Gauss Bonnet formula for manifolds with boundary has an additional term compared to the formula for closed manifolds. This additional term comes from the boundary contribution. A similar result is true for the signature theorem which was proved by Atiyah, Patoudi and Singer in 1974. They showed that the signature theorem requires a correction term coming from the boundary called the Eta invariant. The Eta invariant is a spectral invariant of the signature operator on the boundary. In this talk I will give motivate the definition of the Eta invariant and outline a proof of the signature theorem.
