Infinite loop spaces from operads with homological stability

Autor:	Basterra, Maria, Bobkova, Irina, Ponto, Kate, Tillmann, Ulrike, Yeakel, Sarah
Rok vydání:	2016
Předmět:	Mathematics - Algebraic Topology 18D50 55P47 55P48 57N65
Druh dokumentu:	Working Paper
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. Comment: This paper represents part of the authors' Women in Topology project
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.07791 Zobrazit plný text záznamu View this record from Arxiv