LOCALIZATION TECHNIQUES IN COMPUTATION OF
EQUIVARIANT
-
GROUPS AND EQUIVARIANT CROSS SECTIONS OF
STIEFEL MANIFOLDS
Obiedat, Mohammad
Ph. D., Department of mathematics
Supervisor: Prof. Dr. Turgut Önder
September 1998, 97 pages.
Let
be a finite group and
be a finite -connected
G-CW complex. The main purpose of this dissertation is to find means for
computing the equivariant -groups, ,
and then to obtain solutions for the equivariant cross section problem
of Stiefel manifolds.
We give an alternative method for computing .
We do our computations for the cases:
is a free -space,
is a trivial -space,
and is a one point
set. We find the orders of elements of
for various projective spaces, and then use the results to obtain a partial
solution for the equivariant cross section problem of Stiefel manifolds.
Without using Atiyah-Segal completion theorem,
we prove two methods for computing .
Then we show how to use these methods to find
the orders of elements of ,
and also to find .
Our illustrative example is ,
the complex projective space.
-
GROUPS AND EQUIVARIANT CROSS SECTIONS OF
be a finite group and 
be a finite 
-connected
G-CW complex. The main purpose of this dissertation is to find means for
computing the equivariant 
-groups, 
,
and then to obtain solutions for the equivariant cross section problem
of Stiefel manifolds.
for various projective spaces, and then use the results to obtain a partial
solution for the equivariant cross section problem of Stiefel manifolds.
.
Then we show how to use these methods to find
the orders of elements of 
,
and also to find 
,
the complex projective space.