Diagram spaces and symmetric spectra

详细信息    查看全文

• 作者：Steffen Sagave ; Christian Schlichtkrull
• 关键词：primary ; 55P43 ; secondary ; 55P48
• 刊名：Advances in Mathematics
• 出版年：2012
• 出版时间：October-November, 2012
• 年：2012
• 卷：231
• 期：3-4
• 页码：2116-2193
• 全文大小：601 K

文摘

We present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra. The main motivating examples are the -spaces, which are diagrams indexed by finite sets and injections, and -spaces, which are diagrams indexed by Quillen¡¯s localization construction on the category of finite sets and bijections.

We show that the category of -spaces provides a convenient model for the homotopy category of spaces in which every space can be rectified to a strictly commutative monoid. Similarly, the commutative monoids in the category of -spaces model graded spaces.

Using the theory of -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.