Topology studies spaces and continuous transformations.
3 records · Includes focused interests · How we rate progress
The Alpöge–Claude manuscript claims a compact complex threefold, obtained by completing a modular family of complex two-tori, whose underlying smooth manifold is diffeomorphic to S⁶. Philip Engel supplies a separate geometric exposition and self-contained proof of the construction.
Read original source Original Alpöge–Claude constructionalpo.ge
Original report: 2026-08-23OpenAI claims Lie-group structure for any locally compact second-countable Hausdorff group with a faithful jointly continuous action on a connected finite-dimensional manifold under the stated topological conventions.
Read original source Pinned primary manuscript · family 304github.com
Original report: 2026-10-06OpenAI claims that a hyperbolic group with a two-sphere boundary has a proper cocompact action by isometries on hyperbolic three-space, allowing a finite kernel.
Read original source Pinned primary manuscript · family 246github.com
Original report: 2026-10-06Topology studies spaces and continuous transformations. Group actions and manifold structure require dimension, regularity, and faithfulness conditions.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
Alpöge–Claude reports: a complex structure on the six-sphere
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