This thesis investigates the topology and geometry of hyperbolic knot complements that are commensurable with other knot complements. In chapter 3, we provide an infinite family examples of hyperbolic knot complements commensurable with exactly two other knot complements. In chapter 4, we exhibit an obstruction to knot complements admitting exceptional surgeries in conjunction with hidden symmetries. Finally, in chapter 5, we discuss the role of surfaces embedded in 3-orbifolds as it relates to hidden symmetries. / text

Submitted by Willian Eliseu da Silva null (willianeliseu@hotmail.com) on 2016-10-13T13:56:54Z No. of bitstreams: 1 simulacao_computacional_proteinas.pdf: 3524008 bytes, checksum: 981d0a947d1fa19cb9db73b4f48d993a (MD5) / Rejected by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo a orientação abaixo: O arquivo submetido não contém o certificado de aprovação. Corrija esta informação e realize uma nova submissão com o arquivo correto. Agradecemos a compreensão. on 2016-10-19T17:12:33Z (GMT) / Submitted by Willian Eliseu da Silva null (willianeliseu@hotmail.com) on 2016-10-21T03:19:08Z No. of bitstreams: 1 simulacao_computacional_proteinas.pdf: 3716184 bytes, checksum: a3d8fc2e2a43d95d3033287e0fc1ad93 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-10-21T20:00:33Z (GMT) No. of bitstreams: 1 silva_we_me_bauru.pdf: 3716184 bytes, checksum: a3d8fc2e2a43d95d3033287e0fc1ad93 (MD5) / Made available in DSpace on 2016-10-21T20:00:33Z (GMT). No. of bitstreams: 1 silva_we_me_bauru.pdf: 3716184 bytes, checksum: a3d8fc2e2a43d95d3033287e0fc1ad93 (MD5) Previous issue date: 2016-08-31 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Proteínas são polímeros heterogêneos lineares essenciais a todos os organismos vivos. As proteínas apresentam diversas funções nos organismos, tais como: estruturação, catálise, síntese, transferências, entre tantas outras. Neste trabalho foram estudadas as proteínas que apresentam em suas estruturas nós do tipo 3-1. Foram calculadas as distâncias entre os carbonos alfa dessas proteínas e com estes valores foram traçados os gráficos de distâncias que permitem uma visualização geral da estrutura da proteína. Foram realizadas alterações no nó 31 padrão para que este se ajustasse à estrutura real da proteína na região do nó. A partir do gráfico de distâncias foi possível determinar a estrutura secundária presente na proteína, sendo que a alfa hélice apresenta oscilações de aproximadamente 5,5 angstrons. Com os gráficos de distâncias das proteínas e dos nós matemáticos foi possível comprovar a presença do nó e sua proximidade com a equação proposta. / Proteins are linear heterogeneous polymer essential to all living organisms. The proteins have different functions in organisms, such as: structuring, catalysis, synthesis, transfers, among many others. In this work were studied the proteins that presenting in their structure, type 31 knots. The distances between the alpha carbons of those proteins were calculated and with these values were plotted distances graphs that allow general visualization of the protein structure. Changes were made in the standard knot 31 so that it would fit the actual structure of the protein in the node region. From the distances graph was possible to determine the secondary structure of the protein, wherein the alpha helix presents oscillations proximately 5.5 angstroms. With distances graph from proteins and from mathematical knots was possible to prove the presence of the node and its proximity to the proposed equation. / CNPq: 131771/2014-0

Knot theory and 3-manifold topology are closely intertwined, and few invariants stand so firmly in the intersection of these two subjects as the tunnel number of a knot, denoted t(K). We describe two very general constructions that result in knot and link pairs which are subbaditive with respect to tunnel number under connect sum. Our constructions encompass all previously known examples and introduce many new ones. As an application we describe a class of knots K in the 3-sphere such that, for every manifold M obtained from an integral Dehn filling of E(K), g(E(K))>g(M).

Thesis advisor: Tao Li / This dissertation explores a relationship between fibered knots and Heegaard splittings in closed, connected, orientable three-manifolds. We show that a fibered knot, which has a sufficiently complicated monodromy, induces a minimal genus Heegaard splitting that is unique up to isotopy. Moreover, we show that fibered knots in the three-sphere has complexity at most 3. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

My research is about Rope Design. The design of, but more importantly, by and with the ropes. I have worked with ropes all my life, in many ways; sailing, circus, rigging, knots, etc. They have had a big impact on me and my life. In my research I am looking at what they can do and who or what they can be. On stage, in my practice and in my daily life. With me, as well as without me. I want to find an equal partnership with them, where I acknowledge that we both have agency and where both of us constantly keep changing and learning from each other. I am discovering how they can change my movement and the way I look at the world.

An important issue in the furniture industry is more widespread use of character-marks. The purpose of this research was to gain an in-depth understanding of the critical issues associated with acceptance of character-marked hardwood furniture. This information was beneficial for developing strategies to increase character-mark use by large furniture manufacturers. Although much has been said about the benefits of including more character in hardwood furniture, few large manufacturers have implemented such changes in their products. Personal interviews were conducted with product development personnel to develop case studies for large furniture manufacturers. The case studies centered on the companies' experiences with character-marked furniture. A follow-up mail survey was conducted to validate the case studies. It was found that decisions concerning character-mark use occur throughout the product development process, and involve the design, marketing, and production functions within the company. Companies that were able to fit character-marks within acceptable product concepts, considering such factors as style, finish, and hardware, appeared to have the most success with character-marked furniture in the marketplace. Conjoint analysis was employed to provide quantitative measures of retailers' perceptions of character-marked furniture products. This information was useful for determining the potential for push-type promotion. The dependent measure stimuli were full product profiles (actual wood samples and pictures), presented to respondents during on-site interviews. Retailers preferred furniture with no knots when evaluations were based on buying consideration and relative price. However, there was a linear relationship between preference and knot size, suggesting that opportunities for use of small knots may exist. It was found that character-marks were quite important to the product evaluations, suggesting that character-marks are a salient product feature. In addition to generating preference measures for tangible furniture product attributes, an investigation of the intangible product attributes associated with character-marks was conducted. Rustic, casual, and antique looks were most associated with character-marked furniture. Promotion of character-marked furniture based on environmental and natural material themes did not appear to hold much potential in the minds of manufacturers and retailers. It appears that promotion of character-marked furniture aimed at retailers will have to be based on what character-marks add to the look of wood household furniture. / Ph. D.

Made available in DSpace on 2015-03-26T13:45:36Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1441623 bytes, checksum: 546ade192993fd13d15e3039ab577882 (MD5) Previous issue date: 2013-07-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, we study the classical invariants of Legendrian Knots Theory and we show that these are not complet. To do this we introduce a notion of a Basic Knot Theory like their classical invariants, Thurston-Bennequin number and Maslov number. Then we discuss a new tool developed by Chekanon and denoted by DGA (Differential Graduated Algebra), wich will help us in the proof of the incompletness of classical invariants of legendrian knots. / Neste trabalho, estudaremos os invariantes clássicos da Teoria de Nós Legendreanos e mostraremos que estes não são completos. Para tal introduzimos uma noção básica da Teoria de Nós Legendreanos, assim como seus invariantes clássicos, o número de Thurston-Bennequin e o número de Maslov. Em seguida discutiremos uma nova ferramenta desenvolvida por Chekanov, a Álgebra Diferencial Graduada, denotada por DGA (Differential Graduated Algebra), que nos auxiliar na prova da incompletude dos invariantes clássicos de nós legendreanos.

The 4-genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4-genus and related invariants of homology classes is the Thom conjecture, proved by Kronheimer-Mrowka, and its symplectic extension due to Ozsv´ath-Szab´o, which say that closed symplectic surfaces minimize genus. In this thesis, we prove a relative version of the symplectic capping theorem. More precisely, suppose (X, ω) is a symplectic 4-manifold with contact type bounday ∂X and Σ is a symplectic surface in X such that ∂Σ is a transverse knot in ∂X. We show that there is a closed symplectic 4-manifold Y with a closed symplectic submanifold S such that the pair (X, Σ) embeds symplectically into (Y, S). This gives a proof of the relative version of Symplectic Thom Conjecture. We use this to study 4-genus of fibered knots in S3 . We also prove a relative version of the sufficiency part of Giroux’s criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in S3 . Using this result, we give a criterion for quasipostive fibered knots to be strongly quasipositive. Symplectic convexity disc bundles is a useful tool in constructing symplectic fillings of contact manifolds. We show the symplectic convexity of the unit disc bundle in a Hermitian holomorphic line bundle over a Riemann surface.

[pt] O propósito deste trabalho é apresentar a teoria dos nós legendreanos, que diz respeito a nós tangentes a uma estrutura de contato, assim como demonstrar o Teorema do Número Máximo de Thurston- Bennequin para nós de 2-pontes em termos do polinômio de Kaumman. Iniciamos este trabalho com uma introdução aos nós topológicos. Apresentamos a teoria de nós legendreanos, dando ênfase aos nós legendreanos em R3 tangentes à estrutura de contato canônica neste espa»co. Apresentamos dois invariantes clássicos de nós legendreanos: os números de Thurston- Bennequin e Maslov. Finalmente, obtemos o número máximo de Thurston-Bennequin, motivo de estudos nos dias atuais, para todos os nós legendreanos topologicamente isotópicos aos nós de 2-pontes na estrutura de contato canônica em R3. / [en] The purpose of this work is to present the Theory of the Legendrian knots, which refers to knots tangent to a contact structure, and also to prove the Theorem of the Maximal Thurston-Bennequin number for 2- bridge knots in terms of the Kaumman polynomial.We begin this study with an introduction to topological knots. We present the theory of the Legendrian knots, we emphasize Legendrian knots in R3, knots tangent to the standard contact structure in this space. We present two classical invariants of Legendrian knots, the Thurston-Bennequin and Maslov numbers. Finally we show the maximal Thurston-Bennequin number for Legendrian two- bridge knots in standard contact structure on R3, an active area of current research.

In this paper we explore the slice-ribbon conjecture for some families of pretzel knots. Donaldson's diagonalization theorem provides a powerful obstruction to sliceness via the union of the double branched cover W of B⁴ over a slicing disk and a plumbing manifold P([capital gamma]). Donaldson's theorem classifies all slice 4-strand pretzel knots up to mutation. The correction term is another 3-manifold invariant defined by Ozsváth and Szabó. For a slice knot K the number of vanishing correction terms of Y[subscript K] is at least the square root of the order of H₁(Y[subscript K];Z). Donaldson's theorem and the correction term argument together give a strong condition for 5-strand pretzel knots to be slice. However, neither Donaldson's theorem nor the correction terms can distinguish 4-strand and 5-strand slice pretzel knots from their mutants. A version of the twisted Alexander polynomial proposed by Paul Kirk and Charles Livingston provides a feasible way to distinguish those 5-strand slice pretzel knots and their mutants; however the twisted Alexander polynomial fails on 4-strand slice pretzel knots. / text