|
|||||
|
|
|
|
|
|
|
|
|
On a spectral sequence
for the cohomology of infinite loop spaces
Rune Haugseng and Haynes Miller |
|
Algebraic & Geometric Topology 16 (2016) 2911–2947
|
Abstract |
|
We study the mod- cohomology spectral sequence arising from delooping the Bousfield–Kan cosimplicial space giving the –nilpotent completion of a connective spectrum . Under good conditions its –term is computable as certain nonabelian derived functors evaluated at as a module over the Steenrod algebra, and it converges to the cohomology of . We provide general methods for computing the –term, including the construction of a multiplicative spectral sequence of Serre type for cofibration sequences of simplicial commutative algebras. Some simple examples are also considered; in particular, we show that the spectral sequence collapses at when is a suspension spectrum. |
Keywords
cohomology, infinite loop spaces, spectral sequence
|
Mathematical Subject Classification 2010
Primary: 18G40, 55P47
|
References |
Publication
Received: 13 August 2015
Revised: 23 February 2016
Accepted: 7 March 2016
Published: 7 November 2016
|
Authors |
| Rune Haugseng | |
| Department of Mathematical
Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark |
|
| http://sites.google.com/site/runehaugseng | |
| Haynes Miller | |
| Department of Mathematics Massachusetts Institute of Technology Building 2, Room 106 %Rm 2-237 this seems to be old office number 77 Massachusetts Avenue Cambridge, MA 02139-4307 United States |
|
| http://math.mit.edu/~hrm | |
|
