On the universal pairing for 2-complexes

Khovanov M, Krushkal V, Nicholson J. On the universal pairing for 2-complexes. arXiv:2312.07429. 2023.


The universal pairing for manifolds was defined and shown to lack positivity in dimension 4 by Freedman et al. We prove an analogous result for 2-complexes, and also show that the universal pairing does not detect the difference between simple homotopy equivalence and 3-deformations. The question of whether these two equivalence relations are different for 2-complexes is the subject of the Andrews-Curtis conjecture. We also discuss the universal pairing for higher-dimensional complexes and show that it is not positive.

Last updated on 02/12/2024