On Elementary Invariants of Genus One Knots and Seifert Surfaces

Christine Lescop ()
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Christine Lescop: Institut Fourier, CNRS, Université Grenoble Alpes

Chapter Chapter 20 in Essays on Topology, 2025, pp 437-494 from Springer

Abstract: Abstract This elementary chapter 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 2-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.

Keywords: Knots; 3-manifolds; Seifert surfaces; Homology 3–spheres; Alexander polynomial; Reidemeister torsion; Finite type invariants; 57K10; 57K31; 57K14; 57K16; 57K20 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-81414-3_20

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

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