Homological invariants of strongly invertible knots
This thesis explores the relationship between Khovanov homology and strongly invertible knots through the use of a geometric construction due to Sakuma. On the one hand, new homological and polynomial invariants of strongly invertible knots are extracted from Sakuma's construction, all of which...
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ndltd-bl.uk-oai-ethos.bl.uk-7619612019-02-12T03:16:48ZHomological invariants of strongly invertible knotsSnape, Michael2018This thesis explores the relationship between Khovanov homology and strongly invertible knots through the use of a geometric construction due to Sakuma. On the one hand, new homological and polynomial invariants of strongly invertible knots are extracted from Sakuma's construction, all of which are related to Khovanov homology. Conversely, these invariants are used to study the two-component links and annular knots obtained from Sakuma's construction, the latter of which are almost entirely disjoint from the class of braid closures. Applications include the problem of unknot detection in the strongly invertible setting, the efficiency of an invariant when compared with the η-polynomial of Kojima and Yamasaki, and the use of polynomial invariants to bound the size of the intrinsic symmetry group of a two-component Sakuma link. We also define a new quantity, κA, and conjecture that it is an invariant of strongly invertible knots.QA MathematicsUniversity of Glasgowhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761961http://theses.gla.ac.uk/39015/Electronic Thesis or Dissertation |
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QA Mathematics Snape, Michael Homological invariants of strongly invertible knots |
description |
This thesis explores the relationship between Khovanov homology and strongly invertible knots through the use of a geometric construction due to Sakuma. On the one hand, new homological and polynomial invariants of strongly invertible knots are extracted from Sakuma's construction, all of which are related to Khovanov homology. Conversely, these invariants are used to study the two-component links and annular knots obtained from Sakuma's construction, the latter of which are almost entirely disjoint from the class of braid closures. Applications include the problem of unknot detection in the strongly invertible setting, the efficiency of an invariant when compared with the η-polynomial of Kojima and Yamasaki, and the use of polynomial invariants to bound the size of the intrinsic symmetry group of a two-component Sakuma link. We also define a new quantity, κA, and conjecture that it is an invariant of strongly invertible knots. |
author |
Snape, Michael |
author_facet |
Snape, Michael |
author_sort |
Snape, Michael |
title |
Homological invariants of strongly invertible knots |
title_short |
Homological invariants of strongly invertible knots |
title_full |
Homological invariants of strongly invertible knots |
title_fullStr |
Homological invariants of strongly invertible knots |
title_full_unstemmed |
Homological invariants of strongly invertible knots |
title_sort |
homological invariants of strongly invertible knots |
publisher |
University of Glasgow |
publishDate |
2018 |
url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761961 |
work_keys_str_mv |
AT snapemichael homologicalinvariantsofstronglyinvertibleknots |
_version_ |
1718975144685207552 |