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Abstract:

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.

Registro:

Documento: Artículo
Título:Classical invariants for global actions and groupoid atlases
Autor:Del Hoyo, M.L.; Minian, E.G.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Global actions; Groupoid atlases; Homology; K-Theory; Simplicial objects; Topology; Global actions; Groupoid atlases; Homology; K-Theory; Simplicial objects; Maps
Año:2008
Volumen:16
Número:6
Página de inicio:689
Página de fin:721
DOI: http://dx.doi.org/10.1007/s10485-007-9113-4
Título revista:Applied Categorical Structures
Título revista abreviado:Appl Categorical Struct
ISSN:09272852
CODEN:ACASE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09272852_v16_n6_p689_DelHoyo

Referencias:

  • Abels, H., Holz, S., Higher generation by subgroups (1993) J. Algorithms, 160, pp. 311-341
  • Bak, A., Global actions: The algebraic counterpart of a topological space (1997) Russian Math. Surveys, 5, pp. 955-996
  • Bak, A., Topological methods in algebra, in rings, Hopf algebras and Brauer groups (1998) Lecture Notes in Pure and Appl. Math., 197, pp. 43-54. , Canepeel, S., Verschoren, A. (eds.)
  • Bak, A., Brown, R., Minian, E.G., Porter, T., Global actions, groupoid atlases and applications (2006) J. Homotopy Relat. Struct., 1, pp. 101-167
  • Bass, H., (1968) Algebraic K-Theory, , Benjamin New York
  • Brown, R., (2006) Topology and Groupoids, , Booksurge PLC Charleston
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  • May, J.P., (1999) A Concise Course in Algebraic Topology. Chicago Lectures in Mathematics, , University of Chicago Press Chicago
  • Milnor, J., (1971) Introduction to Algebraic K-Theory. Annals of Mathematics Studies, Vol. 72, , Princeton University Press Princeton
  • Minian, E.G., Generalized cofibration categories and global actions (2000) K-Theory, 20, pp. 37-95
  • Minian, E.G., Lambda-cofibration categories and the homotopy categories of global actions and simplicial complexes (2002) Appl. Categ. Structures, 10, pp. 1-21
  • Porter, T., Geometric aspects of multiagent systems (2003) Electron. Notes Theor. Comput. Sci., 81, pp. 73-98
  • Quillen, D., Higher algebraic K-theory i (1973) Springer LNM, 341, pp. 85-147
  • Segal, G., Classifying spaces and spectral sequence (1968) Inst. Hautes Études Sci. Publ. Math., 34, pp. 105-112
  • Spanier, E., (1966) Algebraic Topology, , Springer Berlin Heidelberg New York
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Citas:

---------- APA ----------
Del Hoyo, M.L. & Minian, E.G. (2008) . Classical invariants for global actions and groupoid atlases. Applied Categorical Structures, 16(6), 689-721.
http://dx.doi.org/10.1007/s10485-007-9113-4
---------- CHICAGO ----------
Del Hoyo, M.L., Minian, E.G. "Classical invariants for global actions and groupoid atlases" . Applied Categorical Structures 16, no. 6 (2008) : 689-721.
http://dx.doi.org/10.1007/s10485-007-9113-4
---------- MLA ----------
Del Hoyo, M.L., Minian, E.G. "Classical invariants for global actions and groupoid atlases" . Applied Categorical Structures, vol. 16, no. 6, 2008, pp. 689-721.
http://dx.doi.org/10.1007/s10485-007-9113-4
---------- VANCOUVER ----------
Del Hoyo, M.L., Minian, E.G. Classical invariants for global actions and groupoid atlases. Appl Categorical Struct. 2008;16(6):689-721.
http://dx.doi.org/10.1007/s10485-007-9113-4