Morse cohomology in a Hilbert space via the Conley index

Open Access


The main theorem of this paper states thatMorse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.


Morse homology Morse–Witten–Floer complex Conley index Seiberg–Witten–Floer homology 

Mathematics Subject Classification

Primary 53D40 Secondary 55N20 


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© The Author(s) 2015

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Authors and Affiliations

  1. 1.Mathematical InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Faculty of Technical Physics and Applied MathematicsGdansk University of TechnologyGdanskPoland

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