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        Braid Floer Homology on Surfaces

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        Thesis Braid Floer homology on Surfaces.pdf (722.2Kb)
        Publication date
        2016
        Author
        Giessen, D. van der
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        Summary
        The Arnold Conjecture gives the existence of 1-periodic solutions of a nondegenerate Hamiltonian system on a compact symplectic manifold. This Conjecture is proved for aspherical manifolds with the use of Floer homology. After this proof, we continue with developing braid Floer homology on surfaces. We look at free and skeleton braids to define braid Floer homology. The skeleton braids are known solutions for the Hamiltonian. The free braids are unknown solutions. Braid Floer homology tells us when the skeleton forces new solutions. For a special class of skeleton and free braids on the torus, I define braid Floer homology completely.
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        https://studenttheses.uu.nl/handle/20.500.12932/23650
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