Classification of Tight Semiflows

Classify all tight semiflows on a fixed sutured manifold, including those with finitely many primitive closed orbits beyond the canonical semiflows on 4-STs and non-longitudinal 2-STs.

Background

The paper identifies canonical semiflows on homology guts and proves uniqueness results for the special sutured-torus components called 4-STs and non-longitudinal 2-STs. It then highlights the broader classification of tight semiflows on a fixed sutured manifold as unresolved, particularly for semiflows with only finitely many primitive closed orbits.

References

The classification of tight semiflows on a fixed sutured manifold is also a natural question. Tsang asks whether one can characterize all tight semiflows that only have finitely many primitive closed orbits, except the canonical ones on 4-STs and non-longitudinal 2-STs.

— Pseudo-Anosov flow and dynamics on guts  (2608.30973 - Huang, 31 Aug 2026) in Section 6, subsection “Characterization of flows on the guts”