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Uncountably many proper homotopy types from self-connected sum at infinity
Uncountable CSI conjecture. There exists an open, one-ended $4$ -manifold $M$ such that CSI of $M$ with itself yields at least $c$ manifolds up to proper homotopy when $c$ is uncoun…
Conjectureopen4-manifolds connected-sum-at-infinity proper-homotopyarXiv posted 2 days ago

Uncountably many proper homotopy types from self-connected sum at infinity