OpenAI reports filtered-product nullity from complex cobordism

For a finite pointed CW pair G ⊂ E and based map v:E→Sᵈ whose restriction to G becomes null after passage to complex cobordism, the restriction of a sufficiently large smash power v∧ℓ to the union where any fixed positive fraction of factors lie in G is stably null.

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OpenAI reports filtered-product nullity from complex cobordism

  • Mathematics

For a finite pointed CW pair G ⊂ E and based map v:E→Sᵈ whose restriction to G becomes null after passage to complex cobordism, the restriction of a sufficiently large smash power v∧ℓ to the union where any fixed positive fraction of factors lie in G is stably null. The paper also derives a boundary-preserving cube compression theorem from a torus-slot bundle embedding of rank strictly below twice the source rank.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

For a finite pointed CW pair G ⊂ E and based map v:E→Sᵈ whose restriction to G becomes null after passage to complex cobordism, the restriction of a sufficiently large smash power v∧ℓ to the union where any fixed positive fraction of factors lie in G is stably null. The paper also derives a boundary-preserving cube compression theorem from a torus-slot bundle embedding of rank strictly below twice the source rank.

Why it matters

If correct, provides a coherent filtered-product vanishing theorem and a geometric compression criterion for arbitrarily large Cartesian powers, including compact metric inputs without a dimension bound.

What counts as progress

Can MU-nullity on one subcomplex force coherent stable nullity across a filtered union of large smash products?

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