1973.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Mathoverflow 1973

Does the 6-sphere $S^6$ admit the structure of a complex manifold?

References:

mathoverflow/1973, asked by user Fetchinson0234.
[Al26] L. Alpöge, A compact complex threefold fibred by tori over the projective line, and the six-sphere (2026), originally shared on X.

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

abbrev Mathoverflow1973.unitSphere The unit n-sphere, defined as Metric.sphere 0 1 in EuclideanSpace ℝ (Fin (n + 1)) line 38 source
Source documentation
The unit n-sphere, defined as Metric.sphere 0 1 in EuclideanSpace ℝ (Fin (n + 1)).

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Set, EuclideanSpace, Real, Fin, HAdd.hAdd, OfNat.ofNat
Proof uses: Metric.sphere, ENNReal
26 instances, coercions and auxiliary constants left out.
```
abbrev unitSphere (n : ℕ) : Set (EuclideanSpace ℝ (Fin (n + 1))) := Metric.sphere 0 1
…
```
theorem Mathoverflow1973.mathoverflow_1973 sorry line 49 source
depends on sorry what this means
Statement uses: Iff, True, Exists, ChartedSpace, EuclideanSpace, Complex, Fin, OfNat.ofNat, Nat, ENNReal, Real, HAdd.hAdd, Mathoverflow1973.unitSphere, Membership.mem, Set, IsManifold, modelWithCornersSelf, WithTop, ENat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
80 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.