Bibliographic record
Abstract
Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps.To each Whitney stratified manifold we assign transversal homotopy monoids, one for each natural number.The assignment is functorial for a natural class of maps which we call stratified normal submersions.When the stratification is trivial the transversal homotopy monoids are isomorphic to the usual homotopy groups.We compute some simple examples and explore the elementary properties of these invariants.We also assign 'higher invariants', the transversal homotopy categories, to each Whitney stratified manifold.These have a rich structure; they are rigid monoidal categories for n > 1 and ribbon categories for n > 2. As an example we show that the transversal homotopy categories of a sphere, stratified by a point and its complement, are equivalent to categories of framed tangles.I am in great debt to John Baez, and to all those who contributed to the discussion on the n-category café, for the idea of studying transversal homotopy theory.I would like to thank Alexey Gorinov and Conor Smyth for many helpful discussions.This work is funded, very generously,
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".