Tesi etd-09202021-182414 |
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Tipo di tesi
Tesi di laurea magistrale
Autore
RIZZI, EDOARDO
URN
etd-09202021-182414
Titolo
Conteggio di superfici essenziali in una 3-varietà
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Martelli, Bruno
Parole chiave
- conteggio
- counting
- essential
- essenziale
- manifold
- normal
- normale
- varietà
Data inizio appello
29/10/2021
Consultabilità
Completa
Riassunto
Let us consider the problem about counting the number of isotopy classes of essential surfaces in a compact, orientable, irriducible, ∂-irriducible 3-manifold M.
Let b(k) the number of isotopy classes of essential surfaces with characteristic equal to k. We say that a generating function is short if it is the quotient of two rational polynomials where the denominator is a product of cyclotomic polynomials.
The main theorem of the thesis states that if M is atoroidal and acylindric and it does not contain closed non-orientable essential surfaces, then the generating function of b(-2k) is short.
Let b(k) the number of isotopy classes of essential surfaces with characteristic equal to k. We say that a generating function is short if it is the quotient of two rational polynomials where the denominator is a product of cyclotomic polynomials.
The main theorem of the thesis states that if M is atoroidal and acylindric and it does not contain closed non-orientable essential surfaces, then the generating function of b(-2k) is short.
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