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Divisibility of twisted Alexander polynomials and fibered knots

Teruaki Kitano, Takayuki Morifuji (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian S L ( 2 , 𝔽 ) -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree 4 g - 2 for a fibered knot of genus  g .

Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.

Maria Rita Casali (2004)

Revista Matemática Complutense

The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...

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