dc.contributor.author	Dovhyi, Serhii
dc.contributor.examiningcommittee	Krepski, Derek (Mathematics) Wang, Xikui (Statistics)	en_US
dc.contributor.supervisor	Clay, Adam (Mathematics)	en_US
dc.date.accessioned	2017-09-18T17:56:19Z
dc.date.available	2017-09-18T17:56:19Z
dc.date.issued	2017
dc.degree.discipline	Mathematics	en_US
dc.degree.level	Master of Science (M.Sc.)	en_US
dc.description.abstract	The topic of study of this thesis belongs both to knot theory and to group theory. A knot is a smooth embedding of a circle in $\mathbb{R}^3$ or $S^3=\mathbb{R}^3\cup\{+\infty\}$. With any knot $K$ we can do an operation which depends on two integer coefficients $p$ and $q$, called $\frac{p}{q}$ Dehn surgery, resulting in a 3-manifold $M$ denoted by $M:=S^3(K,\frac{p}{q})$. A group is left-orderable if it can be given a total strict ordering which is invariant under multiplication from the left. It is hard to understand Dehn surgery geometrically, but algebraically it is clear - the fundamental group $\pi_1(M)$ equals to the fundamental group of the knot complement of $K$ with one relation added. Although the fundamental group of the knot complement is always left-orderable, $\pi_1(M)$ may not be left-orderable. We study left-orderability of $\pi_1(M)$ in case where $K$ is a twisted torus knot.	en_US
dc.description.note	October 2017	en_US
dc.identifier.uri	http://hdl.handle.net/1993/32614
dc.language.iso	eng	en_US
dc.rights	open access	en_US
dc.subject	Knot theory	en_US
dc.subject	Dehn surgery	en_US
dc.subject	Orderable group	en_US
dc.subject	3-manifold	en_US
dc.title	Non-left-orderable surgeries of twisted torus knots	en_US
dc.type	master thesis	en_US

Non-left-orderable surgeries of twisted torus knots

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