arXiv subjects

Eri Hatakenaka

Publications and source records attributed to Eri Hatakenaka.

3 recordsLinked to original sources

arXiv2026

Reconstructing Turaev-Viro Invariants from Four-Fold Simple Branched Covering Presentations

We construct a finite state sum from a link diagram labelled by transpositions. The diagram presents a closed 3-manifold as a four-fold simple branched cover, and the state sum equals the SU(2)-type Turaev-Viro invariant of that manifold. For each admissible colouring of the diagram's edges and complementary regions, a global factor is combined with crossing weights obtained by summing over compatible local colourings. We then sum these products over all diagram colourings. The formula is proved by assembling crossing-wise local triangulations and matching the two state sums.

math.GT↗

arXiv2014

On the graded quotients of the ring of Fricke characters of a free group

First, we study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of a free group acts. Then using it, we define a descending filtration of the IA-automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.

math.GR↗

arXiv2014

On the rings of Fricke characters of free abelian groups

In this paper, we study the structure of the rings of Fricke characters of free abelian groups. More precisely, we consider a descending filtration of ideals in the ring, and give a basis of its graded quotients. Then by using this fact, we show that the ring of Fricke characters of a free aberian group is an integral domain.

math.GR↗