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Arnold conjecture over integers

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arxiv 2209.08599 v1 pith:IVGFM33V submitted 2022-09-18 math.SG math.ATmath.DSmath.GT

Shaoyun Bai , Guangbo Xu This is my paper · ORCID
classification math.SGmath.ATmath.DSmath.GT
keywords hamiltoniannumberbetticonstructingfloergeneralizestotalwork
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For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth global Kuranishi charts. This generalizes a recent work of Abouzaid-McLean-Smith, which might be of independent interest.

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Cited by 4 Pith papers

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