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

57T15 Homology and cohomology of homogeneous spaces of Lie groups

57T35 Applications of Eilenberg-Moore spectral sequences

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