Frank Neumann
On the Cohomology of Homogeneous Spaces of Finite Loop Spaces and the Eilenberg-Moore Spectral Sequence
Preprint series: Mathematica Gottingensis
MSC:
55P35 Loop spaces
55T20 Eilenberg-Moore spectral sequences, See also {57T35}
57T15 Homology and cohomology of homogeneous spaces of Lie groups
57T35 Applications of Eilenberg-Moore spectral sequences, See also {55R20, 55T20}
Abstract: We prove a collapse theorem for the Eilenberg-Moore spectral sequence and
as an application we show, that under certain conditions the cohomology of
a homogeneous space of a connected finite loop space with a maximal rank torsion
free subgroup is concentrated in even degrees and torsionfree, generalizing
classical theorems for compact Lie groups of Borel and Bott.
Keywords: Eilenberg-Moore spectral sequence, finite loop spaces, homogeneous and classifying spaces
Notes: This paper will appear:
F. Neumann: On the Cohomology of Homogeneous Spaces of Finite Loop Spaces
and the Eilenberg-Moore Spectral Sequence,
Journal of Pure and Appl. Algebra