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The Role of Links in the Study of 3-Manifolds

2017
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3-manifolds are spaces that locally resemble Euclidean 3-dimensional space. The study and classification of such manifolds is of central concern in topology and geometry. We introduce the notion of surgery on a link as a means of obtaining 3-manifolds; a deep result of Lickorish and Wallace tells us that all sufficiently nice 3-manifolds can be obtained by such surgery. We then offer a new generalization of a well-known result on how a relationship between links gives information on how their associated zero surgery manifolds are related.

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