2014/02/27 by Dingyu Yang, Yang, Dingyu · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.1402.7008
127 pages, 17 figures; in subsection 9.3, added an explicit construction of Kuranishi embeddings into the fiber product good coordinate system, and made changes to have the fiber product square property, although the bottom-left half of the square is not used later; and made some minor changes
openalex publication_date 2014/02/27 · arxiv created 2014/03/03 · arxiv updated 2014/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.