On elementary invariants of genus one knots and Seifert surfaces

Christine Lescop

doi:10.1007/978-3-031-81414-3_20

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arXiv · 2304.04707

On elementary invariants of genus one knots and Seifert surfaces

Christine Lescop

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Abstract

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.

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Christine Lescop. 2023-04-10. On elementary invariants of genus one knots and Seifert surfaces. https://doi.org/10.1007/978-3-031-81414-3_20

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