References for tubular neighborhoods of (CW or simplicial) complexes embedded in Euclidean space The following is Fernando Muro's comment to this post on MathOverflow:

Any countable group is a colimit of a sequence of finitely presented groups (indexed by the natural numbers). For each of these finitely presented groups, take a finite 2-complex whose fundamental group is that group. Then build the mapping telescope. That can be properly embedded in $\mathbb{R}^5$ (since the 2-complexes are embedable in $\mathbb{R}^4$), I guess, and you can take a tubular neighbourhood, which is your desired manifold.

My question is: How does one take such tubular neighborhoods? I'm only familiar with tubular neighborhoods of smooth submanifolds. In my understanding, a "tubular neighborhood" is some neighborhood that at least deformation retracts to it. But what is the precise definition? Do you have any references for the existence of such neighborhoods, so that the argument above is valid?
Thanks in advance!
 A: A PL topology text such as Sanderson is indeed the way to go, as suggested by @Tyrone. But one can define  somewhat briefly what the regular neighborhood actually is.
To set up the definition, one is given a simplicial complex $X$ and a subcomplex $A \subset X$. And then one defines the regular neighborhood $N(A) \subset X$ to be the subcomplex of the 2nd barycentric subdivision of $X$ consisting of all simplices of $X$ that have nonempty intersection with $A$. The key feature of this construction is that $N(A)$ deformation retracts to $A$ in a canonical fashion. Constructing that deformation retraction is fairly elementary, carried out on a simplex-by-simplex basis  in $N(A)$. 
In the context of that citation from MathOverflow, I think that in order to make it work you want first to make sure that your 2-dimensional mapping telescope $A$ is a locally finite simplicial complex, and then you want to embed it as a subcomplex of a simplicial structure on $\mathbb R^5$ consisting of standard, rectilinear simplexes. Once you've done that, there's still some work to show that $N(A)$ is actually a 5-dimensional submanifold with boundary in $\mathbb R^5$ (in the PL category; and more smoothing work to do if you want the DIFF category instead).
