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Tesi etd-06082015-123156


Tipo di tesi
Tesi di laurea magistrale
Autore
CASTRONOVO, MARCO
URN
etd-06082015-123156
Titolo
Twisted Whitney towers and concordance of links
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Teichner, Peter
controrelatore Prof. Lisca, Paolo
Parole chiave
  • concordance
  • knots and links
  • Milnor invariants
  • quantum invariants
  • Whitney towers
Data inizio appello
17/07/2015
Consultabilità
Completa
Riassunto
In Chapter 1 we explain the theory of Whitney towers in its simplest, framed form and show its connection with a class of link invariants defined by Milnor in his early works and with the problem of deciding whether a link is slice (i.e. concordant to unlink) or not. In Chapter 2 we address some subtler problem regarding twisting in Whitney towers and the corresponding obstruction theory. Twisted towers are used to define a notion of twisted concordance and a corresponding filtration on the set of links. The structure of this filtration is not fully understood yet and it seems to suggest the existence of a new class of concordance invariants generalizing the classical Arf invariant of knots. In Chapter 3 we explain a general procedure to build string link invariants from ribbon Hopf algebras and a recent result of Meilhan and Suzuki describing concordance information contained in the invariant associated to the h-adic quantized universal enveloping algebra of the Lie algebra sl_2. The hope is that quantum invariants coming from other ribbon Hopf algebras could also contain concordance information and be related to the obstruction theory of twisted Whitney towers.
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