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Preprint in the OpenAI Math release

A nondegenerate counterexample to the Morse-number Arnold bound

OpenAI

Abstract

We construct a smooth one-periodic Hamiltonian on a closed symplectic twelve-manifold whose time-one map has fewer fixed points than the manifold's ordinary Morse number. Every fixed point is nondegenerate and has a contractible Hamiltonian trajectory. This disproves the Morse-number form of the Arnold conjecture. The deficit can be arbitrarily large among twelve-dimensional examples.

open until 1 Jan 2028

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