On the integral homology of PSL4(Z{double-struck}) and other arithmetic groups

Mathieu Dutour Sikirić; Graham Ellis; Achill Schürmann

doi:10.1016/j.jnt.2011.05.018

On the integral homology of PSL₄(Z{double-struck}) and other arithmetic groups

Mathieu Dutour Sikirić, Graham Ellis, Achill Schürmann

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

Abstract

We determine the integral homology of PSL₄(Z{double-struck})) in degrees up to 5 and determine its p-part in higher degrees for the primes p≥5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral homology of PGL₃(Z{double-struck})[i]) and PGL₃(Z{double-struck})[exp(2πi/3)]) in degrees up to 5.

Original language	English
Pages (from-to)	2368-2375
Number of pages	8
Journal	Journal of Number Theory
Volume	131
Issue number	12
DOIs	https://doi.org/10.1016/j.jnt.2011.05.018
Publication status	Published - Dec 2011

Keywords

Arithmetic groups
Homology
Perfect forms
Well rounded retract

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10.1016/j.jnt.2011.05.018

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abstract = "We determine the integral homology of PSL4(Z\{double-struck\})) in degrees up to 5 and determine its p-part in higher degrees for the primes p≥5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral homology of PGL3(Z\{double-struck\})[i]) and PGL3(Z\{double-struck\})[exp(2πi/3)]) in degrees up to 5.",

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AU - Ellis, Graham

AU - Schürmann, Achill

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N2 - We determine the integral homology of PSL4(Z{double-struck})) in degrees up to 5 and determine its p-part in higher degrees for the primes p≥5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral homology of PGL3(Z{double-struck})[i]) and PGL3(Z{double-struck})[exp(2πi/3)]) in degrees up to 5.

AB - We determine the integral homology of PSL4(Z{double-struck})) in degrees up to 5 and determine its p-part in higher degrees for the primes p≥5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral homology of PGL3(Z{double-struck})[i]) and PGL3(Z{double-struck})[exp(2πi/3)]) in degrees up to 5.

KW - Arithmetic groups

KW - Homology

KW - Perfect forms

KW - Well rounded retract

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DO - 10.1016/j.jnt.2011.05.018

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EP - 2375

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 12

ER -

On the integral homology of PSL₄(Z{double-struck}) and other arithmetic groups

Abstract

Keywords

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