Infinite loop spaces from operads with homological stability Academic Article uri icon

abstract

  • 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.

published proceedings

  • ADVANCES IN MATHEMATICS

author list (cited authors)

  • Basterra, M., Bobkova, I., Ponto, K., Tillmann, U., & Yeakel, S.

citation count

  • 4

complete list of authors

  • Basterra, Maria||Bobkova, Irina||Ponto, Kate||Tillmann, Ulrike||Yeakel, Sarah

publication date

  • December 2017