1. On elementary invariants of genus one knots and Seifert surfaces
- Author
-
Lescop, Christine
- Subjects
Mathematics - Geometric Topology ,57K10 (Primary) 57K31, 57K14, 57K16, 57K20 (Secondary) - 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., Comment: 54 pages, 12 figures, minor revision, mainly typographical
- Published
- 2023