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# The Enhanced Linking Number and its Applications

## Electronic Theses and Dissertations

### Item Details

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
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