Title: A spectral sequence for string cohomology

Authors: Marcel Bokstedt and Iver Ottosen

AMS Classification numbers: 55N91, 55P35, 18G50

Address of Authors:

Institut for Matematiske Fag
Aarhus Universitet
Ny Munkegade
DK-8000 Aarhus C

Matematisk Afdeling
Koebenhavns Universitet
Universitetsparken 5
DK-2100 Koebenhavn OE

Email address of Authors:

marcel@imf.au.dk
iver@math.ku.dk

Abstract:
Let $X$ be a 1-connected spaces with free loop space $\Lambda X$. 
We introduce two spectral sequences converging towards 
$H^*(\Lambda X;\ZZ /p)$ and $H^*((\Lambda X)_{hS^1};\ZZ /p)$.
The $E_2$-terms are certain non Abelian derived functors applied 
to $H^*(X;\ZZ /p)$. When  $H^*(X;\ZZ /p)$ is a polynomial algebra, 
the spectral sequences collapse for more or less trivial reasons. 
If $X$ is a sphere it is a surprising fact that the spectral 
sequences collapse for $p=2$.