• Augustin Banyaga
  • David Hurtubise
Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 29)


A Morse-Smale function f: M → ℝ. on a finite dimensional compact smooth Riemannian manifold (M, g) gives rise to a chain complex (C * (f), * ), called the Morse-Smale-Witten chain complex (Definition 7.2), whose chains are generated by the critical points of f and whose boundary operator is defined by counting gradient flow lines (with sign).


Manifold Betti 


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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Augustin Banyaga
    • 1
  • David Hurtubise
    • 2
  1. 1.The Pennsylvania State UniversityUniversity ParkUSA
  2. 2.The Pennsylvania State UniversityAltoonaUSA

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