Relative Invariants, Contact Geometry and Open String Invariants

Abstract

In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces ${\bar{\mathcal{M}}}_A(M^{+},C,g,m+\nu ,\mathbf{y},\mathbf{p},(\mathbf{k},\mathfrak{e}))$ and ${\bar{\mathcal{M}}}_A(M,L;g,m+\nu ,\mathbf{y},\mathbf{p},\overrightarrow{\mu })$, prove the compactness of the moduli spaces and the existence of the invariants.

62 pages, 2 figures. Comments welcome. Revise version,58 pages, correct some mistakes