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Pré-Publication, Document De Travail Année : 2023

On elementary invariants of genus one knots and Seifert surfaces

Christine Lescop

Résumé

This elementary article introduces easy-to-manage invariants of genus one knots in homology 3-spheres. To prove their invariance, we investigate properties of an invariant of 3-dimensional genus two homology handlebodies called the Alexander form. The Alexander form of a 3-manifold E with boundary contains all Reidemeister torsions of link exteriors obtained by attaching two-handles along the boundary of E. It is a useful tool for studying Alexander polynomials and Reidemeister torsions. We extract invariants of genus one Seifert surfaces from the Alexander form of their exteriors.

Dates et versions

hal-04095089 , version 1 (11-05-2023)

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Christine Lescop. On elementary invariants of genus one knots and Seifert surfaces. 2023. ⟨hal-04095089⟩
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