Equivariant iterated loop space theory and permutative G-categories

被引:30
作者
Guillou, Bertrand J. [1 ]
May, J. Peter
机构
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
关键词
UNIQUENESS; BAR;
D O I
10.2140/agt.2017.17.3259
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We set up operadic foundations for equivariant iterated loop space theory. We start by building up from a discussion of the approximation theorem and recognition principle for V-fold loop G-spaces to several avatars of a recognition principle for infinite loop G-spaces. We then explain what genuine permutative G-categories are and, more generally, what E-infinity-G-categories are, giving examples showing how they arise. As an application, we prove the equivariant Barratt-Priddy-Quillen theorem as a statement about genuine G-spectra and use it to give a new, categorical proof of the tom Dieck splitting theorem for suspension G-spectra. Other examples are geared towards equivariant algebraic K-theory.
引用
收藏
页码:3259 / 3339
页数:81
相关论文
共 46 条
[1]   Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory [J].
Ando, Matthew ;
Blumberg, Andrew J. ;
Gepner, David ;
Hopkins, Michael J. ;
Rezk, Charles .
JOURNAL OF TOPOLOGY, 2014, 7 (04) :1077-1117
[2]  
[Anonymous], 2002, MEM AM MATH SOC
[3]  
[Anonymous], 1997, OPERADS P RENAISSANC, DOI DOI 10.1090/CONM/202/02588
[4]  
Barratt M.G., 1974, TOPOLOGY, V13, P25
[5]   AN APPROXIMATION THEOREM FOR EQUIVARIANT LOOP-SPACES IN THE COMPACT LIE CASE [J].
CARUSO, J ;
WANER, S .
PACIFIC JOURNAL OF MATHEMATICS, 1985, 117 (01) :27-49
[6]   FIXED SET SYSTEMS OF EQUIVARIANT INFINITE LOOP-SPACES [J].
COSTENOBLE, SR ;
WANER, S .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 326 (02) :485-505
[7]  
DRESS AWM, 1982, LECT NOTES MATH, V966, P59
[8]   Rings, modules, and algebras in infinite loop space theory [J].
Elmendorf, A. D. ;
Mandell, M. A. .
ADVANCES IN MATHEMATICS, 2006, 205 (01) :163-228
[9]  
Elmendorf A D, 1997, Math. Surv. Monogr., V47
[10]  
FIEDOROWICZ Z, 1982, LECT NOTES MATH, V967, P23