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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds.

Symplectic Floer Homology of Area-Preserving Surface Diffeomorphisms and Sharp Fixed Point Bounds.

Cotton-Clay, Andrew Walker

Paperback

General Mathematics

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ISBN10: 1243663375
ISBN13: 9781243663375
Publisher: Proquest Umi Dissertation Pub
Pages: 102
Weight: 0.43
Height: 0.21 Width: 7.44 Depth: 9.69
Language: English
The symplectic Floer homology HF*(&phis;) of a symplectomorphism &phis; Sigma → Sigma encodes data about the fixed points of &phis; using counts of holomorphic cylinders in R x M&phis;, where M &phis; is the mapping torus of &phis;. We give an algorithm to compute HF*(&phis;) for &phis; a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF*( h) for h any orientation-preserving mapping class. Given a closed, oriented surface Sigma, possibly with boundary, and a mapping class g ∈ pi0(Diff+(Sigma, dSigma)), we obtain a sharp lower bound on the number of fixed points of a surface symplectomorphism (i.e. area-preserving map) in the given mapping class, generalizing the Poincare-Birkhoff fixed point theorem. This bound often exceeds that for non-area-preserving maps. These bounds come from Floer homology computations with certain twisted coefficients and a new method for obtaining fixed point bounds on entire symplectic mapping classes on monotone symplectic manifolds from such computations.

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