Homotopy invariance through small stabilizations

We associate an algebra (Formula presented.) to each bornological algebra (Formula presented.). Each symmetric ideal (Formula presented.) of the algebra (Formula presented.) of complex bounded sequences gives rise to an ideal (Formula presented.) of (Formula presented.). We show that all ideals aris...

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Autor principal: Cortiñas, Guillermo Horacio
Publicado: 2015
Materias:
Calkin’s theorem
Crossed product
K-theory
Karoubi’s cone
Operator ideal
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15122891_v10_n3_p459_Abadie
http://hdl.handle.net/20.500.12110/paper_15122891_v10_n3_p459_Abadie
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15122891_v10_n3_p459_Abadie
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spelling paper:paper_15122891_v10_n3_p459_Abadie2023-06-08T16:18:25Z Homotopy invariance through small stabilizations Cortiñas, Guillermo Horacio Calkin’s theorem Crossed product K-theory Karoubi’s cone Operator ideal We associate an algebra (Formula presented.) to each bornological algebra (Formula presented.). Each symmetric ideal (Formula presented.) of the algebra (Formula presented.) of complex bounded sequences gives rise to an ideal (Formula presented.) of (Formula presented.). We show that all ideals arise in this way when (Formula presented.) is the algebra of complex numbers. We prove that for suitable (Formula presented.) , Weibel’s (Formula presented.) -theory of (Formula presented.) is homotopy invariant, and show that the failure of the map from Quillen’s to Weibel’s (Formula presented.) -theory of (Formula presented.) to be an isomorphism is measured by cyclic homology. © 2013, Tbilisi Centre for Mathematical Sciences. Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15122891_v10_n3_p459_Abadie http://hdl.handle.net/20.500.12110/paper_15122891_v10_n3_p459_Abadie
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Calkin’s theorem
Crossed product
K-theory
Karoubi’s cone
Operator ideal
spellingShingle Calkin’s theorem
Crossed product
K-theory
Karoubi’s cone
Operator ideal
Cortiñas, Guillermo Horacio
Homotopy invariance through small stabilizations
topic_facet Calkin’s theorem
Crossed product
K-theory
Karoubi’s cone
Operator ideal
description We associate an algebra (Formula presented.) to each bornological algebra (Formula presented.). Each symmetric ideal (Formula presented.) of the algebra (Formula presented.) of complex bounded sequences gives rise to an ideal (Formula presented.) of (Formula presented.). We show that all ideals arise in this way when (Formula presented.) is the algebra of complex numbers. We prove that for suitable (Formula presented.) , Weibel’s (Formula presented.) -theory of (Formula presented.) is homotopy invariant, and show that the failure of the map from Quillen’s to Weibel’s (Formula presented.) -theory of (Formula presented.) to be an isomorphism is measured by cyclic homology. © 2013, Tbilisi Centre for Mathematical Sciences.
author Cortiñas, Guillermo Horacio
author_facet Cortiñas, Guillermo Horacio
author_sort Cortiñas, Guillermo Horacio
title Homotopy invariance through small stabilizations
title_short Homotopy invariance through small stabilizations
title_full Homotopy invariance through small stabilizations
title_fullStr Homotopy invariance through small stabilizations
title_full_unstemmed Homotopy invariance through small stabilizations
title_sort homotopy invariance through small stabilizations
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15122891_v10_n3_p459_Abadie
http://hdl.handle.net/20.500.12110/paper_15122891_v10_n3_p459_Abadie
work_keys_str_mv AT cortinasguillermohoracio homotopyinvariancethroughsmallstabilizations
_version_ 1768545480706359296

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