Diagram spaces and symmetric spectra
From MaRDI portal
Publication:456797
DOI10.1016/J.AIM.2012.07.013zbMATH Open1315.55007arXiv1103.2764OpenAlexW1995054292MaRDI QIDQ456797
Author name not available (Why is that?)
Publication date: 16 October 2012
Published in: (Search for Journal in Brave)
Abstract: We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the I-spaces, which are diagrams indexed by finite sets and injections, and J-spaces, which are diagrams indexed by the Grayson-Quillen construction on the category of finite sets and bijections. We show that the category of I-spaces provides a convenient model for the homotopy category of spaces in which every E-infinity space can be rectified to a strictly commutative monoid. Similarly, the commutative monoids in the category of J-spaces model graded E-infinity spaces. Using the theory of J-spaces we introduce the graded units of a symmetric ring spectrum. The graded units detect periodicity phenomena in stable homotopy and we show how this can be applied to the theory of topological logarithmic structures.
Full work available at URL: https://arxiv.org/abs/1103.2764
No records found.
No records found.
This page was built for publication: Diagram spaces and symmetric spectra
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q456797)
