3-deformations of 2-complexes and Morse Theory
Ximena Fernández · arXiv (Cornell University) · 2019
We introduce novel combinatorial methods to study 3-deformations of CW-complexes of dimension 2 or, equivalently, $Q^{**}$-transformations of group presentations. Our procedures are based on a new version of Discrete Morse Theory for $n$-deformations. We apply these techniques to show that some known potential counterexamples to the Andrews-Curtis conjecture do satisfy the conjecture.