Embedded contact homology and open book decompositions
Bibliographic record
Abstract
Given a closed oriented contact 3-manifold M, we prove an equivalence between the embedded contact homology of M and a version of embedded contact homology "relative to the boundary", defined on the complement of a tubular neighborhood of a null-homologous knot.This paper can be viewed as the first of a series of papers devoted to proving the isomorphism between Heegaard Floer homology and embedded contact homology.The appendix, written jointly with Yuan Yao, gives a complete proof of Morse-Bott gluing for one-level cascades in embedded contact homology.57K31, 57K33 1. Introduction 3346 2. Review of embedded contact homology 3348 3. Cobordism maps and direct limits 3354 4. Morse-Bott theory 3359 5. Topological constraints on holomorphic curves 3370 6. Construction of contact forms 3375 7. ECH for manifolds with torus boundary 3378 8. ECH of the solid torus 3388 9. Proof of Theorem 1.1.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.179 | 0.018 |
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".