Morse Homology pp 133-198 | Cite as

Morse Homology Theory

Part of the Progress in Mathematics book series (PM, volume 111)


We introduce Morse homology theory by two main theorems about the existence of a canonical boundary operator associated to a given Morse function f and about the existence of canonical isomorphisms between each pair of such Morse complexes. These theorems appear as the essence from the theory on compactness, gluing and orientation which has been developed throughout the last three chapters. It is the isolated trajectories of the time-independent, time-dependent and the λ-parametrized gradient flow which form the crucial features in the core of these main theorems. The following preparatory section describes how we associate respective characteristic signs to these isolated trajectories.


Homology Group Morse Index Morse Function Admissible Pair Homology Theory 
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Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  1. 1.MathematikETH ZentrumZürichSwitzerland

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