TITLE: Reference request for wild 3-manifolds
QUESTION [9 upvotes]: I’m looking for a text on 3-manifolds that focuses on wild/pathological objects, similar to Bing’s work in the field. I know basic algebraic topology (homotopy, homology, cohomology) and have read through Schulten’s Introduction to 3 manifolds. Are there any good texts about these that focus on the geometric aspects more than the algebraic side?

REPLY [8 votes]: As far as I know, there's not really any textbooks on this subject. There's a memoir by Brin and Thickstun, but this is not focussed on geometric aspects of wild manifolds. 
Sylvain Maillot has explored non-compact 3-manifolds, and in particular studied Ricci flow on manifolds of bounded geometry. 
Tommaso Cremaschi has a couple of papers on non-compact 3-manifolds which do not admit a hyperbolic metric. 
In a paper of John Pardon on the Hilbert-Smith conjecture, he analyzes certain wild manifolds with two ends, and shows that the (istopy classes of) closed incompressible surfaces which separate the ends form a lattice. The proof of this uses some geometry of minimal surfaces. 
The literature on wild 3-manifolds is sparse enough that no one has taken up the effort to write a textbook on the subject as far as I know. There is no conjectural classification; indeed it is hard to imagine what such a classification might look like.