Related papers: The topology of Kuranishi atlases
Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Their core idea was to build such…
Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Their core idea was to build such…
Kuranishi structures were introduced to symplectic topology by Fukaya and Ono and recently refined by Joyce, in order to extract homological data from compactified moduli spaces of holomorphic maps in cases where geometric regularization…
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. This paper is a brief introduction to the…
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. Let Y be an orbifold and R a commutative…
'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1106.4882), as the geometric structure on moduli spaces of $J$-holomorphic curves. An alternative to Kuranishi spaces is the…
These notes aim to explain a joint project with Katrin Wehrheim that uses finite dimensional reductions to construct a virtual fundamental class for the Gromov--Witten moduli space of closed genus zero curves. Our method is based on work by…
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…
This article is the second part of the article we promised to write at the end of Section 1 of [FOOO15] (arXiv:1209.4410). (Part I appeared in [Part I] (arXiv:1503.07631).) We discuss the foundation of the virtual fundamental chain and…
This is the second of a series of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. Using the notion of obstruction…
This is a survey of the author's paper arXiv:1409.6908 and in-progress book. 'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1503.07631), as the geometric structure on moduli…
This is the first part of the article we promised at the end of [FOOO13, Section 1]. We discuss the foundation of the virtual fundamental chain and cycle technique, especially its version appeared in [FOn] and also in [FOOO4, Section A1,…
We construct the Kuranishi spaces, or in other words, the versal deformations, for the following classes of connections with fixed divisor of poles $D$: all such connections, as well as for its subclasses of integrable, integrable…
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside an ambient moduli stack of…
The notion of good coordinate system was introduced by Fukaya and Ono in [FOn] in their construction of virtual fundamental chain via Kuranishi structure which was also introduced therein. This notion was further clarified in [FOOO1] in…
We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts. We apply the…
A Kuranishi atlas is a structure used to build a virtual fundamental class on moduli spaces of $J$-holomorphic curves. They were introduced by McDuff and Wehrheim to resolve some of the challenges in this field. This paper completes the…
We introduce $L_{\infty}$-Kuranishi spaces by associating, to each chart, $L_{\infty}[1]$-algebras defined on open neighborhoods of the zero points of the Kuranishi section. We show that these objects collectively form a category, which…
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…
Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach…