LekhoriLekhoriTo finish by making one last addition.
To glue a relatively uncomplicated compact manifold to a manifold of the same dimension along (a component of the latter's boundary).
a. 1997, Rob[ion] Kirby, "Problems in Low-Dimensional Topology", problem 3.21, in, 1997, William H[ilal] Kazez, editor, Geometric Topology, proceedings of the 1993 Georgia International Topology Conference, AMS/IP Studies in Advanced Mathematics 2, American Mathematical Society, →ISBN, part 2, page 163, Let X be an acyclic 2-complex and M an abstract regular neighborhood of X; ∂M_0=S², so cap off to get a homology 3-sphere M³.
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