October 4, 2016
This is a part of my joint work with Oh-Ohta-Ono and is a part of project to rewrite the whole story of virtual fundamental chain in a way easier to use. In general we can construct virtual fundamental chain on (basically all) the moduli space of pseudo-holomorphic curve. It depends on the choices. In this talk I want to provide a statement to clarify which is the data we need to start with and in which sense the resulting structure is well defined. A purpose of writing such statement is then it can be a black box and can be used without looking the proof. Also it is useful to see some properties of it such as its relation to the (target space) group action or compatibility with forgetful map.