Recall the Zeeman's conjecture: if $K$ is a contractible polyhedron of dimension 2, then $K\times I$ has a collapsible subdivision.
Zeeman showed that this implies the Poincaré conjecture in dimension 3 (which is equivalent to a restricted version of Zeeman's conjecture). It also implies the Andrews-Curtis conjecture (again, there is equivalence of a restricted version). In advertising Zeeman's conjecture these seem to be the two main points. (For an example of such an 'advertisement' see these notes.)
Question 1: What are some other interesting consequences of Zeeman's conjecture being (or not being) true?
I have seen an opinion that the conjecture is generally believed to be false.
Question 2: What are the reasons to believe it is false?