Two examples of vanishing and squeezing in K₁
Resumen:
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.
| 2020 | |
| ANII - FCE_3_2018_1_148588 | |
|
Assembly maps Controlled topology Bass-Heller-Swan theorem |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
|
http://nyjm.albany.edu/j/2020/26-28.html
https://nyjm.albany.edu/ https://hdl.handle.net/20.500.12008/33743 |
|
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522889822371840 |
|---|---|
| author | Ellis, Eugenia |
| author2 | Rodríguez Cirone, Emanuel Tartaglia, Gisela Vega, Santiago |
| author2_role | author author author |
| author_facet | Ellis, Eugenia Rodríguez Cirone, Emanuel Tartaglia, Gisela Vega, Santiago |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Ellis Eugenia, Universidad de la República (Uruguay). Facultad de Ingeniería. Rodríguez Cirone Emanuel, UBA, Buenos Aires, Argentina Tartaglia Gisela, UNLP, La Plata, Argentina Vega Santiago, UBA, Buenos Aires, Argentina |
| dc.creator.none.fl_str_mv | Ellis, Eugenia Rodríguez Cirone, Emanuel Tartaglia, Gisela Vega, Santiago |
| dc.date.accessioned.none.fl_str_mv | 2022-09-09T16:53:54Z |
| dc.date.available.none.fl_str_mv | 2022-09-09T16:53:54Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.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. |
| dc.description.sponsorship.none.fl_txt_mv | ANII - FCE_3_2018_1_148588 |
| dc.format.extent.es.fl_str_mv | 29 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Ellis, E., Rodríguez Cirone, E., Tartaglia, G. y otros. "Two examples of vanishing and squeezing in K₁". New York Journal of Mathematics. [en línea]. 2020, vol. 26, pp. 607-635. |
| dc.identifier.eissn.none.fl_str_mv | 1076-9803 |
| dc.identifier.uri.none.fl_str_mv | http://nyjm.albany.edu/j/2020/26-28.html https://nyjm.albany.edu/ https://hdl.handle.net/20.500.12008/33743 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | NYJM |
| dc.relation.ispartof.es.fl_str_mv | New York Journal of Mathematics, vol. 26, 2020, pp. 607-635. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 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 | Assembly maps Controlled topology Bass-Heller-Swan theorem |
| dc.title.none.fl_str_mv | Two examples of vanishing and squeezing in K₁ |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_127d79ee26f73202da0782028e733934 |
| identifier_str_mv | Ellis, E., Rodríguez Cirone, E., Tartaglia, G. y otros. "Two examples of vanishing and squeezing in K₁". New York Journal of Mathematics. [en línea]. 2020, vol. 26, pp. 607-635. 1076-9803 |
| 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:20.500.12008/33743 |
| publishDate | 2020 |
| 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 (CC - By 4.0) |
| spelling | Ellis Eugenia, Universidad de la República (Uruguay). Facultad de Ingeniería.Rodríguez Cirone Emanuel, UBA, Buenos Aires, ArgentinaTartaglia Gisela, UNLP, La Plata, ArgentinaVega Santiago, UBA, Buenos Aires, Argentina2022-09-09T16:53:54Z2022-09-09T16:53:54Z2020Ellis, E., Rodríguez Cirone, E., Tartaglia, G. y otros. "Two examples of vanishing and squeezing in K₁". New York Journal of Mathematics. [en línea]. 2020, vol. 26, pp. 607-635.http://nyjm.albany.edu/j/2020/26-28.htmlhttps://nyjm.albany.edu/https://hdl.handle.net/20.500.12008/337431076-9803Controlled 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.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2022-09-08T22:32:41Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) ERTV20.pdf: 463388 bytes, checksum: 975c67fd0a74ea2b0a199142c7be9325 (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2022-09-09T16:08:44Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) ERTV20.pdf: 463388 bytes, checksum: 975c67fd0a74ea2b0a199142c7be9325 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-09-09T16:53:54Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) ERTV20.pdf: 463388 bytes, checksum: 975c67fd0a74ea2b0a199142c7be9325 (MD5) Previous issue date: 2020ANII - FCE_3_2018_1_14858829 p.application/pdfenengNYJMNew York Journal of Mathematics, vol. 26, 2020, pp. 607-635.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 (CC - By 4.0)Assembly mapsControlled topologyBass-Heller-Swan theoremTwo examples of vanishing and squeezing in K₁Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaEllis, EugeniaRodríguez Cirone, EmanuelTartaglia, GiselaVega, SantiagoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/33743/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/33743/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-838395http://localhost:8080/xmlui/bitstream/20.500.12008/33743/3/license_textd606c60c5d78967c4ed7a729e5bb402fMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Two examples of vanishing and squeezing in K₁ Ellis, Eugenia Assembly maps Controlled topology Bass-Heller-Swan theorem |
| status_str | publishedVersion |
| title | 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_short | Two examples of vanishing and squeezing in K₁ |
| title_sort | Two examples of vanishing and squeezing in K₁ |
| topic | Assembly maps Controlled topology Bass-Heller-Swan theorem |
| url | http://nyjm.albany.edu/j/2020/26-28.html https://nyjm.albany.edu/ https://hdl.handle.net/20.500.12008/33743 |
