Celebratio Mathematica — McDuff

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D. McDuff: “The virtual moduli cycle,” pp. 73–102 in Northern California symplectic geometry seminar (Berkeley and Stanford, CA, 1989–1998). Edited by Y. Eliashberg, D. Fuchs, D. Ratiu, and A. Weinstein. AMS Translation Series 2 196. American Mathematical Society (Providence, RI), 1999. MR 1736215 Zbl 0958.53060 incollection

This article is an attempt to describe one possible construction of the virtual moduli cycle that is used as a tool in the construction of Gromov–Witten invariants for a general symplectic manifold. There are many different versions of this construction. Here I will in the main follow [Liu and Tian 1998; 1999], since their approach (when modified by an idea of Siebert’s) seems to involve the least amount of analysis. However, it does involved quite a bit of topology, some of which they only outline. The aim here is to flesh out the picture and to explain the different ingredients that are needed to make the construction work. We do not try to give full proofs, nor do we work out all the ideas in full generality.

D. Rațiu	Related
Alan Weinstein	Related
Yakov M. Eliashberg	Related
Dmitry Fuchs	Related	Volume