Frank Neumann
Der Satz von Bott für Liesche Schleifenräume und die Eilenberg-Moore-Spektralsequenz
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

57T25 Homology and cohomology of ${H}$-spaces

Abstract: In 1956 Bott proved, using Morse theory, that the
integral cohomology of the quotient of a 1-connected compact
Lie group by its maximal torus is concentrated in even degrees.
In this thesis we generalize the theorem of Bott to a large
class of finite loop spaces and p-compact groups by using
the Eilenberg-Moore spectral sequence and Brown-Peterson
homology instead of Morse theory. We also study torsion
question in the integral cohomology of finite loop spaces
generalizing results of Kac and Toda in the case of compact
Lie groups.

Keywords: Eilenberg-Moore spectarl sequence, finite loop spaces, homogeneous spaces
Notes: This paper is published as PhD thesis, submitted in June 1996
to the Mathematics Faculty of the University of Goettingen.
Goettingen, Math. Inst. der Univ. und Univ. Diss. 1996
SuUB Sigantur: DISS 97 A 9151