Homology Groups of Resulting Manifolds Constructed from Dehn Surgeries

These two notes compute the homology groups of 3-manifolds obtained by Dehn surgery. The first one focuses on surgery along a knot or link in \( S^3 \), while the second generalizes the computation to surgeries inside an arbitrary 3-manifold.

1) Surgery along a knot or link in \( S^3 \)

2️) Surgery inside an arbitrary 3-manifold