Compare lower central and dimension-series constructions

Determine whether the lower central series and dimension series of link groups admit comparisons through constructions based on surfaces, thereby relating Whitney-tower and grope methods to the bar-construction approach.

Background

The paper contrasts Whitney towers and related geometric-topology constructions, which organize link-group information through the lower central series, with bar cohomology, which is organized through the augmentation-ideal or dimension-series filtration.

A comparison between these filtrations at the level of surface-based constructions could connect two major frameworks for concordance invariants and clarify when information detected by one filtration is visible to the other.

References

A tantalizing question is whether there are comparisons to be made between the two central series through surface-level constructions.

— Bar cohomology of links: beyond Milnor invariants  (2609.11009 - Friedman et al., 10 Sep 2026) in Introduction, Section 1, subsection “Alternate perspectives and future work”