Generating series for symmetric product spaces

Abstract

We consider the symmetric product spaces of closed manifolds. We introduce some geometric invariants and the topological properties of symmetric product spaces via the symmetric invariant ones of product spaces and apply to GromovWitten invariants. We examine the symmetric product spaces of the complex projective line, their GromovWitten invariants and compute the generating series induced by their GromovWitten invariants. © 2012 World Scientific Publishing Company.