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Topological and Algebraic Considerations

  • S. Lefschetz
Part of the Applied Mathematical Sciences book series (AMS, volume 16)

Abstract

A complex analytic 2n-manifold M2n is a connected space defined by the following properties:
  1. (1.1)
    It has a finite covering by 2n-cells U,V,...,W each parametrized by n complex coordinates respectively uh,vj,...,wk with metrics defined by
    $$ d_{u}^{2} = {\sum {{u_{h}}\bar{u}} _{h}},...\;. $$
     
  2. (1.2)

    At all points of overlap say of U,V, the vk are holomorphic in the uh.

     

Keywords

Simplicial Complex Algebraic Variety Homology Group Betti Number Algebraic Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • S. Lefschetz
    • 1
  1. 1.Princeton UniversityUSA

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