Floer Homology and low-dimensional topology
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Heegaard diagrams and holomorphic disks
Gromov’s theory of pseudo-holomorphic disks [39] has wide-reaching consequences in symplectic geometry and low-dimensional topology. Our aim here is to describe certain invariants for low-dimensional manifolds built on this theory. The invariants we describe here associate a graded Abelian group to each closed, oriented three-manifold Y , the Heegaard Floer homology of Y . These invariants also...
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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 ...
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