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On a secondary invariant of the hyperelliptic mapping class group

Takayuki Morifuji — 2009

Banach Center Publications

We discuss relations among several invariants of 3-manifolds including Meyer's function, the η-invariant, the von Neumann ρ-invariant and the Casson invariant from the viewpoint of the mapping class group of a surface.

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 $g$ .

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