Topological Invariants of 3-Manifolds with Boundary
Algebraic Topology
2026-03-20 v1
Abstract
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).
Keywords
Cite
@article{arxiv.2107.07920,
title = {Topological Invariants of 3-Manifolds with Boundary},
author = {Luca Di Beo},
journal= {arXiv preprint arXiv:2107.07920},
year = {2026}
}