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A Polyfold Proof of the Arnold Conjecture. (arXiv:1810.06180v1 [math.SG])
来源于:arXiv
We give a detailed proof of the homological Arnold conjecture for
nondegenerate periodic Hamiltonians on general closed symplectic manifolds $M$
via a direct Piunikhin-Salamon-Schwarz morphism. Our constructions are based on
a coherent polyfold description for moduli spaces of pseudoholomorphic curves
in a family of symplectic manifolds degenerating from
$\mathbb{C}\mathbb{P}^1\times M$ to $\mathbb{C} \times M \sqcup
\mathbb{C}^-\times M$, as developed by Fish-Hofer-Wysocki-Zehnder as part of
the Symplectic Field Theory package. The 2011 sketch of this proof was joint
work with Peter Albers, Joel Fish. 查看全文>>