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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Autores principales: Abadie, B., Cortiñas, G.
Formato: JOUR
Materias:
Calkin’s theorem
Crossed product
K-theory
Karoubi’s cone
Operator ideal
Acceso en línea: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
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spelling todo:paper_15122891_v10_n3_p459_Abadie2023-10-03T16:19:31Z Homotopy invariance through small stabilizations Abadie, B. Cortiñas, G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Abadie, B.
Cortiñas, G.
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.
format JOUR
author Abadie, B.
Cortiñas, G.
author_facet Abadie, B.
Cortiñas, G.
author_sort Abadie, B.
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
url http://hdl.handle.net/20.500.12110/paper_15122891_v10_n3_p459_Abadie
work_keys_str_mv AT abadieb homotopyinvariancethroughsmallstabilizations
AT cortinasg homotopyinvariancethroughsmallstabilizations
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