On the generalized Andrews-Curtis-Problem -- A Disproof of the Relative Case
arXiv:2102.03212
Abstract
The generalized Andrews-Curtis Conjecture expects that finite PLCW 2-complexes which are simple-homotopy equivalent, can be 3-deformed into each other. If in addition subcomplexes are required to be kept fix during the deformation, this is not possible.
Theorem and Proof can speak only of Q*-equivalences. Whether this excludes the given relative (AC')-counterexamples, is not yet clear