The cohomology of lattices in sl(2, c)

Autores
Finis, Tobias; Grunewald, Fritz; Tirao, Paulo Andres
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H1(Γ, En), where Γ is a lattice in SL(2,ℂ) and (Formula Presented), n ∈ ℕ ∪ {0}, is one of the standard selfdual modules. In the case Γ = SL(2, O) for the ring of integers O in an imaginary quadratic number field, we make the theory of lifting explicit and obtain lower bounds linear in n. We present a large amount of experimental data for this case, as well as for some geometrically constructed and mostly nonarithmetic groups. The computations for SL(2, O) lead us to discover two instances with nonlifted classes in the cohomology. We also derive an upper bound of size O(n2/log n) for any fixed lattice Γ in the general case. We discuss a number of new questions and conjectures suggested by our results and our experimental data. © A K Peters, Ltd.
Fil: Finis, Tobias. Heinrich-Heine-Universität. Mathematisches Institut; Alemania
Fil: Grunewald, Fritz. Heinrich-Heine-Universität. Mathematisches Institut; Alemania
Fil: Tirao, Paulo Andres. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
AUTOMORPHIC FORMS
COHOMOLOGY OF ARITHMETIC GROUPS
KLEINIAN GROUPS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/189127
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/189127
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The cohomology of lattices in sl(2, c)Finis, TobiasGrunewald, FritzTirao, Paulo AndresAUTOMORPHIC FORMSCOHOMOLOGY OF ARITHMETIC GROUPSKLEINIAN GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H1(Γ, En), where Γ is a lattice in SL(2,ℂ) and (Formula Presented), n ∈ ℕ ∪ {0}, is one of the standard selfdual modules. In the case Γ = SL(2, O) for the ring of integers O in an imaginary quadratic number field, we make the theory of lifting explicit and obtain lower bounds linear in n. We present a large amount of experimental data for this case, as well as for some geometrically constructed and mostly nonarithmetic groups. The computations for SL(2, O) lead us to discover two instances with nonlifted classes in the cohomology. We also derive an upper bound of size O(n2/log n) for any fixed lattice Γ in the general case. We discuss a number of new questions and conjectures suggested by our results and our experimental data. © A K Peters, Ltd.Fil: Finis, Tobias. Heinrich-Heine-Universität. Mathematisches Institut; AlemaniaFil: Grunewald, Fritz. Heinrich-Heine-Universität. Mathematisches Institut; AlemaniaFil: Tirao, Paulo Andres. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaTaylor & Francis2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/189127Finis, Tobias; Grunewald, Fritz; Tirao, Paulo Andres; The cohomology of lattices in sl(2, c); Taylor & Francis; Experimental Mathematics; 19; 1; 1-2011; 29-631058-64581944-950XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10586458.2010.10129067info:eu-repo/semantics/altIdentifier/doi/10.1080/10586458.2010.10129067info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:46:01Zoai:ri.conicet.gov.ar:11336/189127instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:46:02.008CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The cohomology of lattices in sl(2, c)
title The cohomology of lattices in sl(2, c)
spellingShingle The cohomology of lattices in sl(2, c)
Finis, Tobias
AUTOMORPHIC FORMS
COHOMOLOGY OF ARITHMETIC GROUPS
KLEINIAN GROUPS
title_short The cohomology of lattices in sl(2, c)
title_full The cohomology of lattices in sl(2, c)
title_fullStr The cohomology of lattices in sl(2, c)
title_full_unstemmed The cohomology of lattices in sl(2, c)
title_sort The cohomology of lattices in sl(2, c)
dc.creator.none.fl_str_mv Finis, Tobias
Grunewald, Fritz
Tirao, Paulo Andres
author Finis, Tobias
author_facet Finis, Tobias
Grunewald, Fritz
Tirao, Paulo Andres
author_role author
author2 Grunewald, Fritz
Tirao, Paulo Andres
author2_role author
author
dc.subject.none.fl_str_mv AUTOMORPHIC FORMS
COHOMOLOGY OF ARITHMETIC GROUPS
KLEINIAN GROUPS
topic AUTOMORPHIC FORMS
COHOMOLOGY OF ARITHMETIC GROUPS
KLEINIAN GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H1(Γ, En), where Γ is a lattice in SL(2,ℂ) and (Formula Presented), n ∈ ℕ ∪ {0}, is one of the standard selfdual modules. In the case Γ = SL(2, O) for the ring of integers O in an imaginary quadratic number field, we make the theory of lifting explicit and obtain lower bounds linear in n. We present a large amount of experimental data for this case, as well as for some geometrically constructed and mostly nonarithmetic groups. The computations for SL(2, O) lead us to discover two instances with nonlifted classes in the cohomology. We also derive an upper bound of size O(n2/log n) for any fixed lattice Γ in the general case. We discuss a number of new questions and conjectures suggested by our results and our experimental data. © A K Peters, Ltd.
Fil: Finis, Tobias. Heinrich-Heine-Universität. Mathematisches Institut; Alemania
Fil: Grunewald, Fritz. Heinrich-Heine-Universität. Mathematisches Institut; Alemania
Fil: Tirao, Paulo Andres. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description This paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H1(Γ, En), where Γ is a lattice in SL(2,ℂ) and (Formula Presented), n ∈ ℕ ∪ {0}, is one of the standard selfdual modules. In the case Γ = SL(2, O) for the ring of integers O in an imaginary quadratic number field, we make the theory of lifting explicit and obtain lower bounds linear in n. We present a large amount of experimental data for this case, as well as for some geometrically constructed and mostly nonarithmetic groups. The computations for SL(2, O) lead us to discover two instances with nonlifted classes in the cohomology. We also derive an upper bound of size O(n2/log n) for any fixed lattice Γ in the general case. We discuss a number of new questions and conjectures suggested by our results and our experimental data. © A K Peters, Ltd.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/189127
Finis, Tobias; Grunewald, Fritz; Tirao, Paulo Andres; The cohomology of lattices in sl(2, c); Taylor & Francis; Experimental Mathematics; 19; 1; 1-2011; 29-63
1058-6458
1944-950X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/189127
identifier_str_mv Finis, Tobias; Grunewald, Fritz; Tirao, Paulo Andres; The cohomology of lattices in sl(2, c); Taylor & Francis; Experimental Mathematics; 19; 1; 1-2011; 29-63
1058-6458
1944-950X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/10586458.2010.10129067
info:eu-repo/semantics/altIdentifier/doi/10.1080/10586458.2010.10129067
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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