Equivariant K-homology of the classifying space for proper actions
Equivariant K-homology of the classifying space for proper actions
The aim of this doctoral thesis is to explicitly compute the topological side of the Baum-Connes conjecture, that is, the equivariant K-homology of the classifying space for proper actions, for some discrete groups. This is achieved by means of the Bredon homology with coefficients in the representation ring of the corresponding classifying spaces.
In particular, we obtain the K-homology and Bredon homology for SL3(ℤ), GL3(ℤ) and lower-rank (up to three), right-angled and even Co-xeter groups. On the process, we required a Künneth formula for Bredon homology; we present Künneth formulas for the Bredon homology of the product of a G-CW-complex and a H-CW-complex, the direct product of two groups and also versions for relative Bredon homology, and proper actions with coefficients in the representation ring.
We used the mathematical software GAP during our research. We have implemented routines to compute the Bredon homology, with coefficients in the representation ring, of a proper G-CW-complex, and of a Coxeter group from its Coxeter matrix.
University of Southampton
Sánchez-García, Rubén José
2005
Sánchez-García, Rubén José
Sánchez-García, Rubén José
(2005)
Equivariant K-homology of the classifying space for proper actions.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The aim of this doctoral thesis is to explicitly compute the topological side of the Baum-Connes conjecture, that is, the equivariant K-homology of the classifying space for proper actions, for some discrete groups. This is achieved by means of the Bredon homology with coefficients in the representation ring of the corresponding classifying spaces.
In particular, we obtain the K-homology and Bredon homology for SL3(ℤ), GL3(ℤ) and lower-rank (up to three), right-angled and even Co-xeter groups. On the process, we required a Künneth formula for Bredon homology; we present Künneth formulas for the Bredon homology of the product of a G-CW-complex and a H-CW-complex, the direct product of two groups and also versions for relative Bredon homology, and proper actions with coefficients in the representation ring.
We used the mathematical software GAP during our research. We have implemented routines to compute the Bredon homology, with coefficients in the representation ring, of a proper G-CW-complex, and of a Coxeter group from its Coxeter matrix.
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Published date: 2005
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Local EPrints ID: 466004
URI: http://eprints.soton.ac.uk/id/eprint/466004
PURE UUID: 6a8d5f41-a14a-43c9-b2b5-243e7e8b884f
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Date deposited: 05 Jul 2022 03:56
Last modified: 05 Jul 2022 03:56
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Author:
Rubén José Sánchez-García
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