Algebraic invariants of links and 3-manifolds
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The goal of this thesis is to describe certain algebraic invariants of links, and try tomodify them to obtain invariants of 3-manifolds. Racks and quandles are algebraicstructures that were invented to give invariants of knots and links. They generalisethe classical colouring invariants, and a rack or quandle can be associated to any link,known as its fundamental rack or quandle. In this thesis we explain how to modify theconstruction of the fundamental rack to obtain an invariant of 3-manifolds, making useof the fact that every 3-manifold can be obtained by integral Dehn surgery on a linkin the 3-sphere. Finally, we show how to distinguish the 3-sphere from the Poincaréhomology sphere using this invariant.