We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical $2$-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.
Partially supported by a Research Fellowship from the Leverhulme Trust. This work was started at MSRI, Berkeley, where research is supported by the National Science Foundation under Grant No. DMS-1440140.
"Iteration of functions and contractibility of acyclic 2-complexes." Publ. Mat. 65 (1) 309 - 318, 2021. https://doi.org/10.5565/PUBLMAT6512110