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The Enhanced Linking Number and its Applications

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abstract
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.
subject
algebra
homotopy
invariant
isotopy
knot theory
topology
contributor
Palesis, Eleni Panayiota (author)
Parsley, Jason (committee chair)
Howards, Hugh (committee member)
Moore, Frank (committee member)
Mastin, Matt (committee member)
date
2015-06-23T08:35:31Z (accessioned)
2015 (issued)
degree
Mathematics (discipline)
10000-01-01 (liftdate)
embargo
forever (terms)
identifier
http://hdl.handle.net/10339/57091 (uri)
language
en (iso)
publisher
Wake Forest University
title
The Enhanced Linking Number and its Applications
type
Thesis

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