Topological Invariants of 3-Manifolds with Boundary
This paper presents, with explanatory details, the handle decompositions, fundamental groups and homology groups of 3-manifolds, including some knot complements. Hence, along this paper, when the word manifold appears it is implicit that its dimension is 3, except when explicitly generalized for n dimensions, n natural. The results were obtained for: 3-torus, projective space P^3, trefoil (3^1), figure-eight (4^1), cinquefoil (5^1) and three-twist (5^2).
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Algebraic Topology
