OpenAI Math Digest
AI-GENERATED GUIDE

This guide may contain errors or inaccurate explanations. Check important claims and proofs against the original papers.

FIELD GUIDE

Topology

Topology

Official catalogue 304–321.

Open the official catalogue · p. 33 ↗

Catalogues in this field

Official catalogue numbers
305

Counterexamples to disk embedding and Wall’s manifold conjecture

The catalogue treats two four-dimensional disk obstructions: one fixing only the boundary circles, and another also retaining induced normal framings. The latter paper's marked geometry, algebraic potentials, and finite tensor theorem feed directly into the realization problem for finitely presented integral PD4 groups as groups of closed aspherical topological four-manifolds. This guide follows the manuscripts' claims and the connections between their proofs.

All 3 overviews available

The catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.

Explore the synthesis and connections
Proof overviews (3)Official catalogue order
  1. A boundary-only obstruction to four-dimensional disk embedding
  2. A marked tensor obstruction to four-dimensional disk embedding
  3. A PD4 group without an aspherical manifold model

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