ETD system

Electronic theses and dissertations repository

 

Tesi etd-09272016-215950


Thesis type
Tesi di dottorato di ricerca
Author
CARREGA, ALESSIO
URN
etd-09272016-215950
Title
Shadows and quantum invariants
Settore scientifico disciplinare
MAT/03
Corso di studi
MATEMATICA
Commissione
tutor Prof. Martelli, Bruno
Parole chiave
  • S^1xS^2
  • skein spaces
  • Tait conjecture
  • Turaev
  • shadows
  • Kauffman bracket
  • Jones polynomial
  • quantum invariants
  • knot theory
  • 3-torus
Data inizio appello
08/11/2016;
Consultabilità
completa
Riassunto analitico
We investigate quantum invariants and their topolological applications through skein theory and the use of Turaev&#39;s shadows. <br>We study knots and links in 3-manifold different from S^3, in particular we focus on the connected sum #_g(S^1xS^2) of g&gt;=0 copies of S^1xS^2 and on the 3-torus T^3. Our main tools are the Kauffman bracket an the Turaev&#39;s shadows. <br>An introductin and a surey to skein theory and Turaev&#39;s shadows is given. We present all the main open conjectures about topological applications of quantum invariants. <br>Two theorems about links in S^3 are extended to links and colored knotted trivalent graphs in #_g(S^1xS^2). The first one is the Tait conjecture about crossing number and alternating links, and the second one is the Eisermann&#39;s theorem about ribon surfaces. Both are topological applications of the Jones polynomial. <br>We compute the skein space of the 3-torus. <br>Moreover we show the table of knots a links in S^1xSì2 with crossing number up to 3.
File