# Understanding a comment by Thurston

In page 359 (right after Theorem 2.3) of the following paper

Thurston, William P., Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Am. Math. Soc., New Ser. 6, 357-379 (1982). ZBL0496.57005.

W. Thurston states (and I quote)

A hyperbolic structure on the interior of a compact manifold $$M^3$$ has finite volume if and only if $$\partial M^3$$ consists of tori, with the single exception of Example 2.1, which has no hyperbolic structure of finite volume.

His example 2.1 is simply the product of the 2-torus by the closed interval, $$M = \mathbb{T}^2\times I$$.

What did Thurston had in mind when he stated that? Why did he left the solid torus $$\mathbb{D}\times\mathbb{S}^1$$ out of this, say, classification? I ask that to understand if it was just a blunder or if he actually had a reason to exclude this case (which can be obviously obtained by the quotient $$\mathbb{H}^3/\{\tau\}$$, where $$\tau$$ is a parabolic translation in $$\mathbb{H}^3$$)?