Ledger: notes/QUESTIONS-2026-07-19.md §I item 4
Compute the involutive Heegaard Floer homology (Hendricks–Manolescu) of the unit tangent bundle T¹Σ_g at its self-conjugate spin^c class.
Why it's a good entry point. This is flagged in the ledger as "executable with existing technology, computed by no one." The ordinary HF⁺ of these circle bundles is now pinned down — see data/DTAB-PAPER.md, Theorem C (the displaced-tower phenomenon at the extremal Euler number n = 2g−2, i.e. the unit tangent bundle) and Corollary D. The self-conjugate class is exactly the one carrying the unique reduced Floer class, so the involutive refinement is well-posed and concrete.
What's wanted. The involutive package (the ῑ-action and the resulting d̄, d̲ invariants) at that class, at least for g = 2, 3, 4, checked against the direct computations already in the DTAB data.
Relevant material: data/DTAB-PAPER.md, data/DTAB-DATA-2026-07-19.md, scripts/dtab*_calc.py.
Ledger:
notes/QUESTIONS-2026-07-19.md§I item 4Compute the involutive Heegaard Floer homology (Hendricks–Manolescu) of the unit tangent bundle T¹Σ_g at its self-conjugate spin^c class.
Why it's a good entry point. This is flagged in the ledger as "executable with existing technology, computed by no one." The ordinary HF⁺ of these circle bundles is now pinned down — see
data/DTAB-PAPER.md, Theorem C (the displaced-tower phenomenon at the extremal Euler number n = 2g−2, i.e. the unit tangent bundle) and Corollary D. The self-conjugate class is exactly the one carrying the unique reduced Floer class, so the involutive refinement is well-posed and concrete.What's wanted. The involutive package (the ῑ-action and the resulting d̄, d̲ invariants) at that class, at least for g = 2, 3, 4, checked against the direct computations already in the DTAB data.
Relevant material:
data/DTAB-PAPER.md,data/DTAB-DATA-2026-07-19.md,scripts/dtab*_calc.py.