Counter-Examples to Homotopy Detection by TQFTs in Dimensions 6 and Above

A figshare-hosted PDF presents mathematical counter-examples demonstrating the failure of ordinary topological quantum field theories (TQFTs) to detect homotopy equivalence in certain manifolds. The work by David Reutter and Christopher Schommer-Pries constructs pairs of simply connected closed 6-manifolds and extends the result to higher dimensions. The 520.2 KB document was last updated on 2026-05-12.

Use Cases

• Testing the limits of TQFT invariants based on the described counter-example pairs.
• Studying the distinction between diffeomorphism and homotopy equivalence in high-dimensional manifolds.
• Investigating the properties of the formally smooth (FS) bordism category introduced in the paper.
• Analyzing the role of connectivity and spin structures in manifold classification via TQFTs.

Strengths

• The dataset is a focused, peer-reviewed mathematical proof addressing an open question.
• Explicitly constructs counter-examples for dimensions >=6 and non-simply connected 5-manifolds.
• File size is 520.2 KB, making it easily downloadable.

Limitations

• The dataset is a single PDF document; no structured data (e.g., columnar representations of manifolds) is provided.
• Row count is unknown, which may limit suitability assessment for computational analysis.
• Column-level documentation is absent; field semantics must be inferred from the paper's text.

Provenance

Source

figshare, author listed as ETD Depositor.

Collection Method

Likely contains the formal mathematical proof and construction of the counter-examples.

Freshness

Last updated 2026-05-12 14:52:47; freshness should be verified.