polyfolds

The same holds for McDuff and Wehrheim's 'Kuranishi atlases' in arXiv:1508.01556. Using results of Yang on polyfolds and Kuranishi spaces surveyed in arXiv:1510.06849, a compact topological space X with a 'polyfold Fredholm structure' in the sense of Hofer, Wysocki and Zehnder (see e.g. arXiv:1407.3185) can be made into a Kuranishi space #92;bfX uniquely up to equivalence in #92;bfKur. Our Kuranishi spaces are based on the author's theory of Derived Differential Geometry (see e.g. arXiv:1206.4207), the study of classes of derived manifolds and orbifolds that we call 'd-manifolds' and 'd-orbifolds'.

2015, Dominic Joyce, “Kuranishi spaces as a 2-category”, in arXiv