Need references for study of fundamental group of 3-manifold

Question

Can anyone provide references on the study of the fundamental group of 3-manifolds?

The references should be geared for a physicist that has good knowledge of differential geometry and group theory, but is not very proficient in the latter.

Answer 1

I've been studying fundamental groups of 3-manifolds lately, and one of my main references has been Hempel's book 3-Manifolds (Amer. Math. Soc., Vol. 349, 2004), which although somewhat heavy in its content, discusses a lot about the group-theoretic properties of fundamental groups of 3-manifolds.

Otherwise, there's Aschenbrenner et. al.'s 3-Manifold Groups (Zürich: European Math. Soc., Vol. 20, 2015) which is a nice survey of various things known, which in itself contains a myriad of references about the subject.

If you want the differential geometry side of things, Hempel deals with $I$-bundles over surfaces and the like, and if you want the knot theory side of things, then either Rolfsen's Knots and Links (Amer. Math. Soc., Vol. 346, 2003) is a very accessible text, as is Prasolov & Sossinsky's Knots, Links, Braids and 3-Manifolds (Amer. Math. Soc., No. 154, 1997).

There is much overlap in the above texts, and in my opinion Hempel is the most intense read, but the most rewarding, while Prasolov & Sossinsky give a very hands-on approach with lots of beautiful pictures.