Bull. Austral. Math. Soc. 72(1) pp.7--15, 2005.
A strong excision theorem for
generalised Tate cohomology
N. Mramor Kosta |
Supported in part by the Ministry for Education, Science and Sport of the Republic of Slovenia Research Program No. 101-509.
Abstract
We consider the analogue of the fixed point
theorem of A. Borel in the context of Tate cohomology. We show that
for general compact Lie groups G
the Tate cohomology of a G-CW
complex X with coefficients in a
field of characteristic 0 is in general
not isomorphic to the cohomology of the fixed point set, and thus
the fixed point theorem does not apply. Instead, the following
excision theorem is valid: if X'
is the subcomplex of all G-cells
of orbit type G/H where
dim H > 0, and
V is a ring such that for every
finite isotropy group H the order
|H| is invertible in V, then
(X;V) 
(X';V). In the
special cases G = 
, the circle
group, and G = 
, the group
of unit quaternions, a more elementary geometric proof, using a
cellular model of
U is given.
(X;V) (X';V). In the
special cases G = , the circle
group, and G = , the group
of unit quaternions, a more elementary geometric proof, using a
cellular model of
U is given.Click to download PDF of this article (free access until July 2006)
or get the no-frills version
[an error occurred while processing this directive]| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2162289 | Z'blatt-MATH: 02212181 |
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