Article (Scientific journals)
The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions
Bui, Anh Tuan; Rahm, Alexander; Wendt, Matthias
2019In Journal of Pure and Applied Algebra, 223 (7), p. 2872-2888
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Keywords :
Cohomology of arithmetic groups
Abstract :
[en] We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell–Tate or Bredon homology, one needs cell complexes where cell stabilizers fix their cells pointwise. We provide two algorithms computing an efficient subdivision of a complex to achieve this rigidity property. Applying these algorithms to available cell complexes for PSL_4(Z) provides computations of Farrell–Tate cohomology for small primes as well as the Bredon homology for the classifying spaces of proper actions with coefficients in the complex representation ring.
Research center :
Mathematics Reseach Unit
Disciplines :
Mathematics
Author, co-author :
Bui, Anh Tuan;  University of Science - Ho Chi Minh City, Vietnam > Faculty of Math & Computer Science
Rahm, Alexander ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Wendt, Matthias;  Leibniz-Universitaet Hannover > Institut fuer Algebraische Geometrie
External co-authors :
yes
Language :
English
Title :
The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions
Publication date :
July 2019
Journal title :
Journal of Pure and Applied Algebra
ISSN :
1873-1376
Publisher :
Elsevier, Netherlands
Volume :
223
Issue :
7
Pages :
2872-2888
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR6543139 - Computational Aspects Of Modular Forms And P-adic Galois Representations, 2012 (01/08/2013-31/07/2016) - Gabor Wiese
Name of the research project :
INTER/DFG/FNR/12/10/COMFGREP
Funders :
Gabor Wiese's Université du Luxembourg grant AMFOR
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