Relative Invariants, Contact Geometry and Open String Invariants

preprint2015arXivOpen access

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 MˉA(M+,C,g,m+ν,y,p,(k,e))\bar{\mathcal{M}}_{A}(M^{+},C,g,m+ν,{\bf y},{\bf p},(\mathbf{k},\mathfrak{e})) and MˉA(M,L;g,m+ν,y,p,μ→)\bar{\mathcal{M}}_{A}(M,L;g,m+ν,{\bf y},{\bf p},\overrightarrowμ), prove the compactness of the moduli spaces and the existence of the invariants.

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