Algebraic kk-theory and the KH-isomorphism conjecture

Ellis, Eugenia - Rodríguez Cirone, Emanuel

Resumen:

We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for the KH-isomorphism conjecture introduced by Bartels-Lück in terms of equivariant algebraic kk-groups.


Detalles Bibliográficos
2022
ANII - FCE_3_2018_1_148588
Bivariant algebraic K-theory
Equivariant homology
Homotopy Ktheory
Quillen model categories
Inglés
Universidad de la República
COLIBRI
https://arxiv.org/abs/2205.04558
https://hdl.handle.net/20.500.12008/33733
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author Ellis, Eugenia
author2 Rodríguez Cirone, Emanuel
author2_role author
author_facet Ellis, Eugenia
Rodríguez Cirone, Emanuel
author_role author
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dc.contributor.filiacion.none.fl_str_mv Ellis Eugenia, Universidad de la República (Uruguay). Facultad de Ingeniería.
Rodríguez Cirone Emanuel, UBA, Buenos Aires, Argentina
dc.creator.none.fl_str_mv Ellis, Eugenia
Rodríguez Cirone, Emanuel
dc.date.accessioned.none.fl_str_mv 2022-09-09T16:40:20Z
dc.date.available.none.fl_str_mv 2022-09-09T16:40:20Z
dc.date.issued.none.fl_str_mv 2022
dc.description.abstract.none.fl_txt_mv We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for the KH-isomorphism conjecture introduced by Bartels-Lück in terms of equivariant algebraic kk-groups.
dc.description.sponsorship.none.fl_txt_mv ANII - FCE_3_2018_1_148588
dc.format.extent.es.fl_str_mv 42 p.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Ellis, E. y Rodríguez Cirone, E. Algebraic kk-theory and the KH-isomorphism conjecture. [Preprint]. Publicado en : Mathematics (math.KT-K-Theory and Homology), 2022, pp. 1-42. .arXiv:2205.04558
dc.identifier.uri.none.fl_str_mv https://arxiv.org/abs/2205.04558
https://hdl.handle.net/20.500.12008/33733
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.ispartof.es.fl_str_mv Mathematics (math.KT-K-Theory and Homology), arXiv:2205.04558, may. 2022, pp. 1-42.
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.es.fl_str_mv Bivariant algebraic K-theory
Equivariant homology
Homotopy Ktheory
Quillen model categories
dc.title.none.fl_str_mv Algebraic kk-theory and the KH-isomorphism conjecture
dc.type.es.fl_str_mv Preprint
dc.type.none.fl_str_mv info:eu-repo/semantics/preprint
dc.type.version.none.fl_str_mv info:eu-repo/semantics/submittedVersion
description We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for the KH-isomorphism conjecture introduced by Bartels-Lück in terms of equivariant algebraic kk-groups.
eu_rights_str_mv openAccess
format preprint
id COLIBRI_208d329d73ab463c09051e00eee66e3a
identifier_str_mv Ellis, E. y Rodríguez Cirone, E. Algebraic kk-theory and the KH-isomorphism conjecture. [Preprint]. Publicado en : Mathematics (math.KT-K-Theory and Homology), 2022, pp. 1-42. .arXiv:2205.04558
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
network_acronym_str COLIBRI
network_name_str COLIBRI
oai_identifier_str oai:colibri.udelar.edu.uy:20.500.12008/33733
publishDate 2022
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
spelling Ellis Eugenia, Universidad de la República (Uruguay). Facultad de Ingeniería.Rodríguez Cirone Emanuel, UBA, Buenos Aires, Argentina2022-09-09T16:40:20Z2022-09-09T16:40:20Z2022Ellis, E. y Rodríguez Cirone, E. Algebraic kk-theory and the KH-isomorphism conjecture. [Preprint]. Publicado en : Mathematics (math.KT-K-Theory and Homology), 2022, pp. 1-42. .arXiv:2205.04558https://arxiv.org/abs/2205.04558https://hdl.handle.net/20.500.12008/33733We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for the KH-isomorphism conjecture introduced by Bartels-Lück in terms of equivariant algebraic kk-groups.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2022-09-09T05:40:36Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) ER22.pdf: 563067 bytes, checksum: ef41bcaaaa207422ffd2495b657084d2 (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2022-09-09T16:35:17Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) ER22.pdf: 563067 bytes, checksum: ef41bcaaaa207422ffd2495b657084d2 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-09-09T16:40:20Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) ER22.pdf: 563067 bytes, checksum: ef41bcaaaa207422ffd2495b657084d2 (MD5) Previous issue date: 2022ANII - FCE_3_2018_1_14858842 p.application/pdfenengarXivMathematics (math.KT-K-Theory and Homology), arXiv:2205.04558, may. 2022, pp. 1-42.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Bivariant algebraic K-theoryEquivariant homologyHomotopy KtheoryQuillen model categoriesAlgebraic kk-theory and the KH-isomorphism conjecturePreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaEllis, EugeniaRodríguez Cirone, EmanuelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/33733/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/33733/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Algebraic kk-theory and the KH-isomorphism conjecture
Ellis, Eugenia
Bivariant algebraic K-theory
Equivariant homology
Homotopy Ktheory
Quillen model categories
status_str submittedVersion
title Algebraic kk-theory and the KH-isomorphism conjecture
title_full Algebraic kk-theory and the KH-isomorphism conjecture
title_fullStr Algebraic kk-theory and the KH-isomorphism conjecture
title_full_unstemmed Algebraic kk-theory and the KH-isomorphism conjecture
title_short Algebraic kk-theory and the KH-isomorphism conjecture
title_sort Algebraic kk-theory and the KH-isomorphism conjecture
topic Bivariant algebraic K-theory
Equivariant homology
Homotopy Ktheory
Quillen model categories
url https://arxiv.org/abs/2205.04558
https://hdl.handle.net/20.500.12008/33733

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