2026-09-20T15:29:08Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/570912026-09-02T11:50:30Zcom_10339_14934col_10339_38132

Palesis, Eleni Panayiota 2015-06-23T08:35:31Z 2015 https://wakespace.lib.wfu.edu/handle/10339/57091 A \emph{knot} is the image of an embedding of $S^1$ into $\R^3$, and a \emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with classifying knots and links, and we discuss three notions of equivalence. \emph{Homotopy} is a weak equivalence that classifies links only up to number of components. \emph{Link homotopy} is stronger and preserves a notion of inter-component linking. \emph{Isotopy} is the strongest class of equivalence that preserves all notions of intra-component knotting and inter-component linking. en Wake Forest University algebra homotopy invariant isotopy knot theory topology The Enhanced Linking Number and its Applications Thesis Parsley, Jason Howards, Hugh Moore, Frank Mastin, Matt Mathematics forever 10000-01-01 open.access