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A strong excision theorem for generalised Tate cohomology

Published online by Cambridge University Press:  17 April 2009

N. Mramor Kosta
N. Mramor Kosta
Affiliation:
Institute for Mathematics, Physics, Mechanics, Faculty of Computer and Information Science, University of Ljubljana, Slovenia, e-mail: [email protected]
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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 . In the special cases G = 𝕋, the circle group, and G = 𝕌, the group of unit quaternions, a more elementary geometric proof, using a cellular model of is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 7 - 15
Copyright
Copyright © Australian Mathematical Society 2005

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