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Morse Homology pp 103-132 | Cite as

Orientation

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

Abstract

Summing up the analytical foundational results we have developed up to this stage, we notice that this knowledge about the trajectory spaces of the time-independent and time-dependent negative gradient flow enables us already to build a Morse homology theory with coefficients in the field ℤ2. However, in order to admit arbitrary coefficient groups, i.e. coefficients in ℤ, we still have to accomplish more elaborate results concerning the characteristic intersection numbers for the unparametrized trajectories. Referring to the introduction, we may deduce these intersection numbers from a comparison of the canonical orientation of the intersection manifold \( W^u (x) \cap |W^s \left( y \right) \approx \mathcal{M}_{x,y} \) by the negative gradient field with some coherent orientation related to the critical points.

Keywords

Equivalence Class Fredholm Operator Admissible Pair Trajectory Space Constant Operator 
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 Basel AG 1993

Authors and Affiliations

  1. 1.MathematikETH ZentrumZürichSwitzerland

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