# Floer theory and low dimensional topology

```@article{Mcduff2005FloerTA,
title={Floer theory and low dimensional topology},
author={Dusa Mcduff},
journal={Bulletin of the American Mathematical Society},
year={2005},
volume={43},
pages={25-42}
}```
• D. Mcduff
• Published 6 October 2005
• Mathematics
• Bulletin of the American Mathematical Society
The new 3and 4-manifold invariants recently constructed by Ozsváth and Szabó are based on a Floer theory associated with Heegaard diagrams. The following notes try to give an accessible introduction to their work. In the first part we begin by outlining traditional Morse theory, using the Heegaard diagram of a 3-manifold as an example. We then describe Witten’s approach to Morse theory and how this led to Floer theory. Finally, we discuss Lagrangian Floer homology. In the second part, we define…
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