Bredon-Illman cohomology with actions of totally disconnected groups

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• 作者：Peilin Shi (1)
  Lingzhen Dong (1)
  
  1. Department of Mathematics ; Taiyuan University of Technology ; Taiyuan ; 030024 ; China
  
• 关键词：Bredon ; Illman cohomology with local coefficients ; group action ; totally disconnected group ; exact sequence ; 55N91
• 刊名：Frontiers of Mathematics in China
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：10
• 期：2
• 页码：367-375
• 全文大小：187 KB
• 参考文献：1. Bredon G. Introduction to Compact Transformation Groups. New York and London: Academic Press, 1972
  2. tom Dieck T. Transformation Groups. Berlin: Walter de Gruyter, 1987 CrossRef
  3. Illman S. Equivariant Singular Homology and Cohomology I. Mem Amer Math Soc, No 156. Providence: Amer Math Soc, 1975, 1鈥?4
  4. Illman S. Actions of totally disconnected groups and equivariant singular homology. Topology Appl, 2010, 157: 2659鈥?678 CrossRef
  5. Mukherjee A, Mukherjee G. Bredon-Illman cohomology with local coefficients. Quart J Math Oxford (2), 1996, 47: 199鈥?19 CrossRef
  6. Shi P. Actions of totally disconnected groups and equivariant singular cohomology. Results Math, 2011, 59: 63鈥?1 CrossRef
  7. Spanier E. Algebraic Topology. New York: McGraw-Hill, 1966
  8. Whitehead G. Elements of Homotopy Theory. Berlin: Springer-Verlag, 1978 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

We study the Bredon-Illman cohomology with local coefficients for a G-space X in the case of G being a totally disconnected, locally compact group. We prove that any short exact sequence of equivariant local coefficients systems on X gives a long exact sequence of the associated Bredon-Illman cohomology groups with local coefficients.