Classical invariants for global actions and groupoid atlases

A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to the notion of groupoid atlas. In this paper we define and i...

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Detalles Bibliográficos
Autores principales: del Hoyo, Matías L., Minian, Elias Gabriel
Publicado: 2008
Materias:
Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Topology
Maps
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09272852_v16_n6_p689_DelHoyo
http://hdl.handle.net/20.500.12110/paper_09272852_v16_n6_p689_DelHoyo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09272852_v16_n6_p689_DelHoyo
record_format dspace
spelling paper:paper_09272852_v16_n6_p689_DelHoyo2023-06-08T15:51:49Z Classical invariants for global actions and groupoid atlases del Hoyo, Matías L. Minian, Elias Gabriel Global actions Groupoid atlases Homology K-Theory Simplicial objects Topology Global actions Groupoid atlases Homology K-Theory Simplicial objects Maps A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to the notion of groupoid atlas. In this paper we define and investigate homotopy invariants of global actions and groupoid atlases, such as the strong fundamental groupoid, the weak and strong nerves, classifying spaces and homology groups. We relate all these new invariants to classical constructions in topological spaces, simplicial complexes and simplicial sets. This way we obtain new combinatorial formulations of classical and non classical results in terms of groupoid atlases. © 2007 Springer Science+Business Media B.V. Fil:Del Hoyo, M.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Minian, E.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09272852_v16_n6_p689_DelHoyo http://hdl.handle.net/20.500.12110/paper_09272852_v16_n6_p689_DelHoyo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Topology
Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Maps
spellingShingle Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Topology
Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Maps
del Hoyo, Matías L.
Minian, Elias Gabriel
Classical invariants for global actions and groupoid atlases
topic_facet Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Topology
Global actions
Groupoid atlases
Homology
K-Theory
Simplicial objects
Maps
description A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to the notion of groupoid atlas. In this paper we define and investigate homotopy invariants of global actions and groupoid atlases, such as the strong fundamental groupoid, the weak and strong nerves, classifying spaces and homology groups. We relate all these new invariants to classical constructions in topological spaces, simplicial complexes and simplicial sets. This way we obtain new combinatorial formulations of classical and non classical results in terms of groupoid atlases. © 2007 Springer Science+Business Media B.V.
author del Hoyo, Matías L.
Minian, Elias Gabriel
author_facet del Hoyo, Matías L.
Minian, Elias Gabriel
author_sort del Hoyo, Matías L.
title Classical invariants for global actions and groupoid atlases
title_short Classical invariants for global actions and groupoid atlases
title_full Classical invariants for global actions and groupoid atlases
title_fullStr Classical invariants for global actions and groupoid atlases
title_full_unstemmed Classical invariants for global actions and groupoid atlases
title_sort classical invariants for global actions and groupoid atlases
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09272852_v16_n6_p689_DelHoyo
http://hdl.handle.net/20.500.12110/paper_09272852_v16_n6_p689_DelHoyo
work_keys_str_mv AT delhoyomatiasl classicalinvariantsforglobalactionsandgroupoidatlases
AT minianeliasgabriel classicalinvariantsforglobalactionsandgroupoidatlases
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