Abstract. This article is an introductory description of work-in-progress. Here is presented a short review of the Floer homology, especially of its topological aspects. In analogy with Morse homology we look at the three theories: symplectic, instantonic and Seiberg-Witten cases. Finally, I emphasize some features and describe a few directions for investigation.
AMSclassification. 55N35, 58D27, 57R57, 58E05, 58E15, 58-02
Keywords. Floer homology, 3-manifolds, Morse theory, Seiberg-Witten equations