The Enhanced Linking Number and its Applications

A \emph{knot} is the image of an embedding of S¹ into \R³, 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.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2015

Author dc:creator

• Palesis, Eleni Panayiota

• algebra

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/57091

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/57091