Zero modes,boundary conditions and anomalies on the lattice and in the continuum

We examine the connection, and occasional lack of it, between zero modes and anomalies in lattice and continuum models. In particular we discuss the index theorem for the polyacetylene problem and for two-dimensional Kogut-Susskind/Kähler-Dirac fermions, paying special attention to boundary effects which may be important in simulations on small lattices.