The index formula for Cauchy-Riemann operators on surfaces with boundary punctures

Abstract: I will discuss the proof of the index formula (which generalizes an argument of Taubes), and then give applications of the formula by computing expected dimensions for moduli spaces of holomorphic curves which appear in Relative Symplectic Field Theory. A special example is provided by counting holomorphic curves in the 1 jet space of a smooth manifold, which establishes a link between classical Morse theory and Relative Symplectic Field Theory.