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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-10112022-164318


Tipo di tesi
Tesi di laurea magistrale
Autore
DI PRISA, ALESSIO
URN
etd-10112022-164318
Titolo
Equivariant concordance of strongly invertible knots
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Lisca, Paolo
Parole chiave
  • algebraic concordance
  • equivariant concordance
  • equivariant signature
  • equivariantly slice knot
  • knot concordance
  • strongly invertible knots
Data inizio appello
28/10/2022
Consultabilità
Non consultabile
Data di rilascio
28/10/2025
Riassunto
The main subject of this thesis is the study of the equivariant concordance group of directed strongly invertible knots, introduced by Sakuma.

Considering a particular type of spanning surfaces for strongly invertible knots, we define a new invariant for equivariant concordance, namely a homomorphism from the equivariant concordance group to an equivariant version of the Witt group of the field of rational numbers.
Then, we investigate its relation with previously known invariants, and in particular we show that from this invariant one can naturally retrieve an equivariant version of the knot signature for strongly invertible knots, defined recently by Alfieri, Boyle and Issa.

Finally, we prove that the equivariant concordance group is not abelian, by exhibiting an infinite family of nontrivial commutators, answering a conjecture attributed to Sakuma.
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