Sistemas de Cartan-Eilenberg en K-teoría Equivariante Torcida

• Espinoza, Jesús F. ^[1] ; Ramos, Rafael R. ^[1]
  1. [1] Universidad de Sonora

     Universidad de Sonora

     México

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 7, Nº. 1, 2020 (Ejemplar dedicado a: January - July), págs. 29-41
• Idioma: español
• DOI: 10.17268/sel.mat.2020.01.04
• Títulos paralelos:
  • Cartan-Eilenberg Systems in Twisted Equivariant K-Theory
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El objetivo de este trabajo es mostrar de manera explícita la construcción de un sistema de Cartan-Eilenberg para los grupos de K-teoría equivariante torcida sobre un G-complejo celular finito, con G un grupo finito.Dicho sistema define una sucesio´n espectral cuya segunda página es dada por la cohomología de Cech asociada a una pregavilla de representaciones proyectivas de grupos de isotropía.

  • English

    The goal of this paper is to show explicitly the construction of a Cartan-Eilenberg system for the twisted equivariant K-theory groups of a finite G-CW complex, with G a finite group. Such a system defines a spectralsequence, whose second page is given by the Cˇech cohomology of a presheaf associated to projective representations of isotropy groups.

• Referencias bibliográficas
  • Adem A, Ruan Y. Twisted Orbifold K-Theory. Comm. Math. Phys. 2003; 237(3): 533–556.
  • Atiyah M, Hirzebruch F. Vector bundles and homogeneous spaces. Amer. Math. Soc. Symp. in Pure Math. 1961; 3: 7–38.
  • Atiyah M, Segal G. Twisted K-Theory. Ukr. Mat. Visn. 2004; 1(3): 287–330.
  • Bárcenas N, Espinoza J, Uribe B, Velázquez M. Segal’s spectral sequence in twisted equivariant K-theory for proper and discrete actions. Proceedings...
  • Bárcenas N, Espinoza J, Joachim M, Uribe B. Universal twist in equivariant K-theory for proper and discrete actions. Proceedings of the London...
  • Cartan H, Eilenberg S. Homological algebra. Princeton Landmarks in Mathematics, 1956.
  • Dwyer C. Twisted equivariant K-theory for proper actions of discrete groups. K-Theory. 2008; 38: 95–111.
  • Eilenberg S, Steenrod N. Foundations of algebraic topology. Princeton University Press, 1952.
  • Espinoza J, Uribe B. Topological properties of the unitary group. JP Journal of Geometry and Topology. 2014; 16(1): 45–55.
  • Espinoza J. K-Teoría Equivariante Torcida. PhD thesis, UNAM, 2013.
  • Espinoza J. K-teoría equivariante torcida. Memorias de la XXI Semana de Investigación y Docencia en Matemáticas. Universidad de Sonora, 2011.
  • Freed D, Hopkins J, Teleman C. Loop groups and twisted K-theory I. Journal of Topology. 2011; 4(4): 737–798.
  • Hatcher A. Algebraic Topology. Cambridge, New York, NY., 2002.
  • Karpilovsky G. Projective Representations of Finite Groups. Monographs in Pure and Applied Mathematics 94. Marcel Dekker, Inc., New York and...
  • Karpilovsky G. Group Representations, vol. 2 of North-Holland Mathematics Studies 177. Elsevier Science Publishers, Amsterdam, The Netherlands,...
  • May J, Sigurdsson J. Parametrized Homotopy Theory. Mathematical surveys and monographs, American Mathematical Society, 2006.
  • McCleary J. User’s Guide to Spectral Sequences. Wilmington, Delaware (U.S.A.), 1985.
  • Schultz R. Homotopy decompositions of equivariant function spaces. II. Math. Z. 1973; 132: 69–90.
  • Segal G. Classifying spaces and spectral sequences. Publications Mathematiques de Inst. Hautes ´ Etudes Sci. Publ. Math. 1968; 34: 105–112.
  • Segal G. Equivariant K-Theory. Publications Mathematiques de Inst. Hautes Études Sci. Publ. Math. 1968; 34: 129–151.
  • Simms D. Topological aspects of the projective unitary group. Proc. Camb. Phil. Soc. 1970; 68: 57–60.
  • Uribe B. Group actions on DG-Manifolds and Exact Courant Algebroids. Communications in Mathematical Physics. 2013; 318(1): 35–67. https://doi.org/10.1007/s00220-013-1669-2