On tunnel number degeneration and 2-string free tangle decompositions

On tunnel number degeneration and 2-string free tangle decompositions

This dissertation is on a study of 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by mor...

Full description

Bibliographic Details
Main Author: Nogueira, João Miguel Dias Ferreira
Format: Others
Language:English
Published: 2012
Subjects:
Tunnel number
Degeneration ratio
Prime knots
2-string free tangle decompositions
Online Access:http://hdl.handle.net/2152/ETD-UT-2011-12-4617
id ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2011-12-4617
record_format oai_dc
spelling ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2011-12-46172015-09-20T17:05:43ZOn tunnel number degeneration and 2-string free tangle decompositionsNogueira, João Miguel Dias FerreiraTunnel numberDegeneration ratioPrime knots2-string free tangle decompositionsThis dissertation is on a study of 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one: t(K_1#K_2)≥ t(K_1)+t(K_2)-1, for K_1 and K_2 prime knots. We also study 2-string free tangle decompositions of links with tunnel number two and obtain an equivalent statement to the one on knots. Further observations on tunnel number and essential tangle decompositions are also made.text2012-02-21T20:59:40Z2012-02-21T20:59:40Z2011-122012-02-21December 20112012-02-21T20:59:53Zthesisapplication/pdfhttp://hdl.handle.net/2152/ETD-UT-2011-12-46172152/ETD-UT-2011-12-4617eng
collection NDLTD
language English
format Others
sources NDLTD
topic Tunnel number
Degeneration ratio
Prime knots
2-string free tangle decompositions
spellingShingle Tunnel number
Degeneration ratio
Prime knots
2-string free tangle decompositions
Nogueira, João Miguel Dias Ferreira
On tunnel number degeneration and 2-string free tangle decompositions
description This dissertation is on a study of 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one: t(K_1#K_2)≥ t(K_1)+t(K_2)-1, for K_1 and K_2 prime knots. We also study 2-string free tangle decompositions of links with tunnel number two and obtain an equivalent statement to the one on knots. Further observations on tunnel number and essential tangle decompositions are also made. === text
author Nogueira, João Miguel Dias Ferreira
author_facet Nogueira, João Miguel Dias Ferreira
author_sort Nogueira, João Miguel Dias Ferreira
title On tunnel number degeneration and 2-string free tangle decompositions
title_short On tunnel number degeneration and 2-string free tangle decompositions
title_full On tunnel number degeneration and 2-string free tangle decompositions
title_fullStr On tunnel number degeneration and 2-string free tangle decompositions
title_full_unstemmed On tunnel number degeneration and 2-string free tangle decompositions
title_sort on tunnel number degeneration and 2-string free tangle decompositions
publishDate 2012
url http://hdl.handle.net/2152/ETD-UT-2011-12-4617
work_keys_str_mv AT nogueirajoaomigueldiasferreira ontunnelnumberdegenerationand2stringfreetangledecompositions
_version_ 1716822377102311424

Similar Items