If a smooth almost complex structure on a closed connected smooth four-manifold is tamed by a symplectic form, then the same almost complex structure is compatible with some smooth symplectic form.
If a smooth almost complex structure on a closed connected smooth four-manifold is tamed by a symplectic form, then the same almost complex structure is compatible with some smooth symplectic form.
If a smooth almost complex structure on a closed connected smooth four-manifold is tamed by a symplectic form, then the same almost complex structure is compatible with some smooth symplectic form.
If correct, settles Donaldson’s general tamed-to-compatible existence question in real dimension four.
Does every tamed almost complex structure on a closed four-manifold admit a compatible symplectic form?
Publication dates and editorial changes.
OpenAI reports taming implies compatibility in four dimensions
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