MathDB2 problems
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Characterization of 3-manifolds whose H2 classes are represented by embedded spheres
Compression-theorem characterization conjecture. The 3-manifolds with this realization property are exactly the 3-manifolds covered by Compression Theorem (2).
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Compression uniqueness in S2 times S2
Codimension-two compression conjecture. Any two such embeddings are isotopic; equivalently, the Codimension Two Compression Theorem should hold without its assumptions.