Topological and Algebraic Considerations

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


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.



Simplicial Complex Algebraic Variety Homology Group Betti Number Algebraic Topology 
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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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