Braids, knots and links

• Ano de defesa: 2023
• Autor(a) principal: Fiorotto, Sophia Lopes Ribeiro
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Alexanders Theorem; Braids; Links; Markov Theorem; Nós; Teorema de Alexander; Teorema de Markov; Tranças
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-12102023-194738/

The theory of braids and knots offers a captivating and intuitive avenue for exploring a diverse array of tools in the algebraic topology. We aim to use the context of braids and links to provide a path of study on algebraic topology and exploring important results in the area such as Alexander and Markovs Theorem. This thesis explores braid theorys fundamental aspects, including various definitions of braid groups, equivalence notions, and invariants. It also provides basic notion and results from knot theory, such as invariants and Seifert Surfaces. Moreover, we investigate the relationship between braids and knots. Alexanders Theorem establishes that every knot or link in S 3 can be represented as a closed braid, while Markovs theorem provides insight into the relationship braids generating a given knot share.