Infinite loop spaces from operads with homological stability
| Autor: | Kate Ponto, Ulrike Tillmann, Irina Bobkova, Maria Basterra, Sarah Yeakel |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics General Mathematics 02 engineering and technology Stability result Homology (mathematics) Mathematics::Algebraic Topology 01 natural sciences symbols.namesake 18D50 55P47 55P48 57N65 020901 industrial engineering & automation Infinite loop Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Mathematics::Symplectic Geometry Mathematics Riemann surface 010102 general mathematics Moduli space Stability conditions symbols Diffeomorphism |
| Zdroj: | Advances in Mathematics. 321:391-430 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2017.09.036 |
| Popis: | Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space operads in the sense that the group completions of their algebras are infinite loop spaces. The recent, strong homological stability results of Galatius and Randal-Williams for moduli spaces of even dimensional manifolds can be used to construct examples of operads with homological stability. As a consequence the map to $K$-theory defined by the action of the diffeomorphisms on the middle dimensional homology can be shown to be a map of infinite loop spaces. This paper represents part of the authors' Women in Topology project |
| Databáze: | OpenAIRE |
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