| dc.description.abstract | The goal of this thesis is to describe certain algebraic invariants of links, and try to
modify them to obtain invariants of 3-manifolds. Racks and quandles are algebraic
structures that were invented to give invariants of knots and links. They generalise
the 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 the
construction of the fundamental rack to obtain an invariant of 3-manifolds, making use
of the fact that every 3-manifold can be obtained by integral Dehn surgery on a link
in the 3-sphere. Finally, we show how to distinguish the 3-sphere from the Poincaré
homology sphere using this invariant. | |
