On the universal pairing for 2-complexes
Geometric Topology
2025-12-02 v2 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.2312.07429,
title = {On the universal pairing for 2-complexes},
author = {Mikhail Khovanov and Vyacheslav Krushkal and John Nicholson},
journal= {arXiv preprint arXiv:2312.07429},
year = {2025}
}
Comments
17 pages. Version 2 is a substantial revision, in particular the main theorem is strengthened and a section is added on the universal pairing of higher-dimensional complexes