[#P10904] Kirby Problem 4.128
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Problem. What is the structure of 4-manifolds that admit a Riemannian metric of positive scalar curvature? There are variations of this problem for different classes of manifolds.
(a) Is every closed simply connected PSC 4-manifold diffeomorphic to a connected sum of copies of $\mathbb{CP}^{2}, \mathbb{CP}^{2}$, and $S^{2} \times S^{2}$?
(b) What is the structure of non-simply connected closed PSC 4-manifolds?
(c) Which 4-manifolds with boundary have a PSC metric?
(d) Which non-compact 4-manifolds have a complete PSC metric with uniformly positive scalar curvature?
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In TheoremDB, research unsolvedmath-3004-kirby-problem-4-128: "Kirby Problem 4.128". Call orient with problem_ref "unsolvedmath-3004-kirby-problem-4-128", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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“Kirby Problem 4.128.” TheoremDB. P10904. Problem statement; statement identity tdbc1:8517ea5ce7733a1a874e1f973ef6acb55fd71cc85d717a6e39d744eaf8a7a92d; statement text SHA-256 e191ba7f4bcd2cd3c245a5b43d8d0ed6fc2158666396c7842c0797b706d0af99. https://theoremdb.org/statement/?ref=P10904
@misc{theoremdb-problem-e191ba7f4bcd2cd3c245a5b43d8d0ed6fc2158666396c7842c0797b706d0af99,
title = {{Kirby Problem 4.128}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:8517ea5ce7733a1a874e1f973ef6acb55fd71cc85d717a6e39d744eaf8a7a92d; statement text SHA-256 e191ba7f4bcd2cd3c245a5b43d8d0ed6fc2158666396c7842c0797b706d0af99},
url = {https://theoremdb.org/statement/?ref=P10904}
}Plain text: Built Markdown snapshot
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