Technical details on Kuranishi structure and virtual fundamental chain

Abstract

This is an expository article on the theory of Kuranishi structure and is based on a series of pdf files we uploaded for the discussion of the google group named `Kuranishi' (with its administrator H. Hofer). There we replied to several questions concerning Kuranishi structure raised by K. Wehrheim. At this stage we submit this article to the e-print arXiv, all the questions or objections asked in that google group were answered, supplemented or confuted by us. We first discuss the abstract theory of Kuranishi structure and virtual fundamental chain/cycle. This part can be read independently from other parts. We then describe the construction of Kuranishi structure on the moduli space of pseudoholomorphic curves, including the complete analytic detail of the gluing construction as well as the smoothness of the resulting Kuranishi structure. The case of S^1 equivariant Kuranishi structure which appears in the study of time independent Hamiltonian and the moduli space of Floer's equation is included.

257 pages. arXiv admin note: substantial text overlap with arXiv:1208.1340 by other authors

Cited by in corpus (6)

• Wrapped Floer cohomology and Lagrangian correspondences
• $SO(3)$-Floer homology of 3-manifolds with boundary 1
• The Gromov-Witten axioms for symplectic manifolds via polyfold theory
• Shrinking good coordinate systems associated to Kuranishi structures
• Automatic transversality in contact homology I: Regularity
• Lagrangian correspondences and the generalized Viterbo restriction functor