Efficient and general algorithmic computation of gnarledness invariants

Determine whether geometric gnarledness can be computed efficiently and whether an algorithm exists to compute the algebraic gnarledness or the cohomological lifting volume of marked free Z-chain complexes of finite type.

Background

The paper proves that geometric gnarledness of a finite simplicial complex is algorithmically computable. It does not establish computational efficiency for that algorithm.

The authors also distinguish the geometric invariant from the algebraic gnarledness and the cohomological lifting volume, and explicitly state that their algorithmic computability for finite-type marked Z-chain complexes is unknown.

References

Geometric gnarledness is algorithmically computable (though it is not clear whether this can be done efficiently). In contrast, we do not know whether this is true for the algebraic gnarledness or the cohomological lifting volume of marked $Z$-chain complexes of finite type.

— Quantitative chain extensions and integral cohomological fillings  (2610.02987 - Hofmann et al., 2 Oct 2026) in Paragraph following Example on simplicial volume comparison, Section 5.3