Galatius, Søren; Randal-Williams, Oscar Moduli spaces of manifolds: a user’s guide. (English) Zbl 1476.57058 Miller, Haynes (ed.), Handbook of homotopy theory. Boca Raton, FL: CRC Press. CRC Press/Chapman Hall Handb. Math. Ser., 443-485 (2020). Summary: The Handbook of homotopy theory has been reviewed in [Zbl 1468.55001].Summary: We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.For the entire collection see [Zbl 1468.55001]. Cited in 3 ReviewsCited in 3 Documents MSC: 57R90 Other types of cobordism 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R56 Topological quantum field theories (aspects of differential topology) 55P47 Infinite loop spaces 57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes 55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology Keywords:characteristic classes; diffeomorphism groups; homological stability; moduli spaces Citations:Zbl 1468.55001 PDFBibTeX XMLCite \textit{S. Galatius} and \textit{O. Randal-Williams}, in: Handbook of homotopy theory. Boca Raton, FL: CRC Press. 443--485 (2020; Zbl 1476.57058) Full Text: DOI arXiv