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).

Classifying spaces for knots: new bridges between knot theory and algebraic number theory

PASINI, FEDERICO WILLIAM
2016

Abstract

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.
WEIGEL, THOMAS STEFAN
Classifying spaces, homology, knots
MAT/02 - ALGEBRA
English
MATEMATICA PURA E APPLICATA - 23R
28
2014/2015
(2016). Classifying spaces for knots: new bridges between knot theory and algebraic number theory. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2016).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/129230
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