In this thesis we discuss how, in the context of knot theory, the classifying space of a knot group for the family of meridians arises naturally. We provide an explicit construction of a model for that space, which is particularly nice in the case of a prime knot. We then show that this classifying space controls the behaviour of the finite branched coverings of the knot. We present a 9-term exact sequence for knot groups that strongly resembles the Poitou-Tate exact sequence for algebraic number fields. Finally, we show that the homology of the classifying space behaves towards the former sequence as Shafarevich groups do towards the latter.
(2016). Classifying spaces for knots: new bridges between knot theory and algebraic number theory. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2016).
Autori: | |
Tutore: | WEIGEL, THOMAS STEFAN |
Data di pubblicazione: | 13-set-2016 |
Titolo: | Classifying spaces for knots: new bridges between knot theory and algebraic number theory |
Settore Scientifico Disciplinare: | MAT/02 - ALGEBRA |
Lingua: | English |
Corso di dottorato: | MATEMATICA PURA E APPLICATA - 23R |
Ciclo: | 28 |
Anno Accademico: | 2014/2015 |
Citazione: | (2016). Classifying spaces for knots: new bridges between knot theory and algebraic number theory. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2016). |
Parole Chiave (Inglese): | Classifying spaces, homology, knots |
Appare nelle tipologie: | 07 - Tesi di dottorato Bicocca post 2009 |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
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phd_unimib_712909.pdf | Tesi dottorato | Doctoral thesis | Open Access Visualizza/Apri |