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Dingyu Yang

Publications and source records attributed to Dingyu Yang.

20 records · Page 2Linked to original sources

arXiv2015

Virtual harmony

This article serves a few purposes. First of all, it reviews polyfold--Kuranishi correspondence I (http://arxiv.org/abs/1402.7008) and previews and samples some results from four papers I have been preparing. It is also a written-up and expanded version of a talk I gave at a symplectic conference in Chengdu on June 28, 2015, and it intends to provide bridges and compatibility between various pairs of virtual techniques and to demonstrate some unity among various technical viewpoints in the constructions of structures on moduli spaces in symplectic geometry. More precisely, the abstract perturbative structures (or interchangeably, virtual structures) present in each virtual theory discussed in this paper (and sometimes even the way they essentially originate in applications) are identified pairwise in a way that intertwines the (non-)perturbation mechanisms. To be more helpful to readers and not get them buried under technicalities and notations, we give the ideas and appropriate level of details so that the results will be clear to the relevant experts; meanwhile the ideas of each virtual machinery and how they are related should come through to more application-minded readers so that they might get encouraged to read papers on a given virtual machinery and possibly apply it to remove some technical assumptions in their results. It is meant to be a service to the symplectic community.

math.SG↗

arXiv2014

The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures

This is the first paper in a series which proposes and develops the polyfold Fredholm structure--Kuranishi structure correspondence, identifying these two abstract perturbative structures which are indispensable for constructing and understanding symplectic invariants in the most general settings. In this paper, I present my version of the theory of Kuranishi structures in full generality. This theory is independent of all the choices made in the construction (including the choices of good coordinate systems); and it uses the equivalence of Kuranishi structures as the germ to capture the intrinsic underlying structure to which the perturbation theory descends. This is the first theory in the literature that has these two properties. This choice-independent theory is essential for canonically and functorially identifying the polyfold Fredholm theory of Hofer-Wysocki-Zehnder with the theory of Kuranishi structures. The next two papers in this series will be on the forgetful functor and the globalization functor in the respective directions of the polyfold--Kuranishi correspondence, as well as illustrating the use of the correspondence with a few sample applications.

math.SG↗