Extension to normal pseudomanifolds

Extend the balanced-genus bounds, computations, and classification problems formulated for PL manifolds to normal \(d\)-pseudomanifolds.

Background

The balanced genus is defined for balanced normal pseudomanifolds as well as for PL manifolds. The paper develops its principal lower-bound and characterization results in the manifold setting, leaving the analogous questions for the broader class of normal pseudomanifolds unresolved.

References

Question 6.4. Since the balanced genus can be defined not only for PL d-manifolds but also for normal d-pseudomanifolds, it would be worthwhile to extend the above problems to the setting of normal pseudomanifolds.

— Balanced genus and a lower bound theorem for balanced 3- and 4-manifolds  (2503.06133 - Basak et al., 8 Mar 2025) in Question 6.4, Section 6, p. 15