Two examples of vanishing and squeezing in K1

Autores
Ellis, Eugenia; Rodríguez Cirone, Emanuel Darío; Tartaglia, Gisela; Vega, Santiago Javier
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K1. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K1; this follows from the well-known result of Bass, Heller and Swan.
Fil: Ellis, Eugenia. Universidad de la República; Uruguay
Fil: Rodríguez Cirone, Emanuel Darío. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Tartaglia, Gisela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Vega, Santiago Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
ASSEMBLY MAPS
CONTROLLED TOPOLOGY
BASS-HELLER-SWAN THEOREM
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:11336/136985
Acceder
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spelling Two examples of vanishing and squeezing in K1Ellis, EugeniaRodríguez Cirone, Emanuel DaríoTartaglia, GiselaVega, Santiago JavierASSEMBLY MAPSCONTROLLED TOPOLOGYBASS-HELLER-SWAN THEOREMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K1. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K1; this follows from the well-known result of Bass, Heller and Swan.Fil: Ellis, Eugenia. Universidad de la República; UruguayFil: Rodríguez Cirone, Emanuel Darío. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Tartaglia, Gisela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Vega, Santiago Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaState University of New York2020-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/136985Ellis, Eugenia; Rodríguez Cirone, Emanuel Darío; Tartaglia, Gisela; Vega, Santiago Javier; Two examples of vanishing and squeezing in K1; State University of New York; New York Journal of Mathematics; 26; 6-2020; 607-6351076-9803CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://nyjm.albany.edu/j/2020/26-28.htmlinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1907.06135info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:58:38Zoai:ri.conicet.gov.ar:11336/136985instacron: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:34982025-11-12 09:58:38.827CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Two examples of vanishing and squeezing in K1
title Two examples of vanishing and squeezing in K1
spellingShingle Two examples of vanishing and squeezing in K1
Ellis, Eugenia
ASSEMBLY MAPS
CONTROLLED TOPOLOGY
BASS-HELLER-SWAN THEOREM
title_short Two examples of vanishing and squeezing in K1
title_full Two examples of vanishing and squeezing in K1
title_fullStr Two examples of vanishing and squeezing in K1
title_full_unstemmed Two examples of vanishing and squeezing in K1
title_sort Two examples of vanishing and squeezing in K1
dc.creator.none.fl_str_mv Ellis, Eugenia
Rodríguez Cirone, Emanuel Darío
Tartaglia, Gisela
Vega, Santiago Javier
author Ellis, Eugenia
author_facet Ellis, Eugenia
Rodríguez Cirone, Emanuel Darío
Tartaglia, Gisela
Vega, Santiago Javier
author_role author
author2 Rodríguez Cirone, Emanuel Darío
Tartaglia, Gisela
Vega, Santiago Javier
author2_role author
author
author
dc.subject.none.fl_str_mv ASSEMBLY MAPS
CONTROLLED TOPOLOGY
BASS-HELLER-SWAN THEOREM
topic ASSEMBLY MAPS
CONTROLLED TOPOLOGY
BASS-HELLER-SWAN THEOREM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K1. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K1; this follows from the well-known result of Bass, Heller and Swan.
Fil: Ellis, Eugenia. Universidad de la República; Uruguay
Fil: Rodríguez Cirone, Emanuel Darío. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Tartaglia, Gisela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Vega, Santiago Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in K1. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of K1; this follows from the well-known result of Bass, Heller and Swan.
publishDate 2020
dc.date.none.fl_str_mv 2020-06
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/11336/136985
Ellis, Eugenia; Rodríguez Cirone, Emanuel Darío; Tartaglia, Gisela; Vega, Santiago Javier; Two examples of vanishing and squeezing in K1; State University of New York; New York Journal of Mathematics; 26; 6-2020; 607-635
1076-9803
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136985
identifier_str_mv Ellis, Eugenia; Rodríguez Cirone, Emanuel Darío; Tartaglia, Gisela; Vega, Santiago Javier; Two examples of vanishing and squeezing in K1; State University of New York; New York Journal of Mathematics; 26; 6-2020; 607-635
1076-9803
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://nyjm.albany.edu/j/2020/26-28.html
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1907.06135
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
application/pdf
dc.publisher.none.fl_str_mv State University of New York
publisher.none.fl_str_mv State University of New York
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 13.25334

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