Harmonic forms and spinors on the Taub-bolt space

This paper studies the space of L² harmonic forms and L² harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find all L² zero modes of D̸ A , the Dirac operator twisted by an arbitrary L² harmonic connection A, and independently compute the index of D̸ A . We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we generalise known results concerning harmonic spinors on Euclidean Schwarzschild.