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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todo:paper_09272852_v16_n6_p689_DelHoyo2023-10-03T15:46:54Z Classical invariants for global actions and groupoid atlases Del Hoyo, M.L. Minian, E.G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, M.L. Minian, E.G. 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. |
format |
JOUR |
author |
Del Hoyo, M.L. Minian, E.G. |
author_facet |
Del Hoyo, M.L. Minian, E.G. |
author_sort |
Del Hoyo, M.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 |
url |
http://hdl.handle.net/20.500.12110/paper_09272852_v16_n6_p689_DelHoyo |
work_keys_str_mv |
AT delhoyoml classicalinvariantsforglobalactionsandgroupoidatlases AT minianeg classicalinvariantsforglobalactionsandgroupoidatlases |
_version_ |
1782026456379949056 |