Cohomology of buildings and finiteness properties of $\widetilde {A}_n$-groups
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- by Jacqui Ramagge and Wayne W. Wheeler PDF
- Trans. Amer. Math. Soc. 354 (2002), 47-61 Request permission
Abstract:
Borel and Serre calculated the cohomology of the building associated to a reductive group and used the result to deduce that torsion-free $S$-arithmetic groups are duality groups. By replacing their group-theoretic arguments with proofs relying only upon the geometry of buildings, we show that Borel and Serre’s approach can be modified to calculate the cohomology of any locally finite affine building. As an application we show that any finitely presented $\widetilde {A}_n$-group is a virtual duality group. A number of other finiteness conditions for $\widetilde {A}_n$-groups are also established.References
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Additional Information
- Jacqui Ramagge
- Affiliation: Department of Mathematics, University of Newcastle, NSW 2308 Callaghan, Australia
- MR Author ID: 352868
- Email: jacqui@maths.newcastle.edu.au
- Wayne W. Wheeler
- Affiliation: Center for Communications Research, 4320 Westerra Court, San Diego, California 92117
- Email: wheeler@member.ams.org
- Received by editor(s): March 29, 2000
- Published electronically: August 21, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 47-61
- MSC (2000): Primary 13D25, 20J06
- DOI: https://doi.org/10.1090/S0002-9947-01-02818-5
- MathSciNet review: 1859024