A Construction of Rational Seifert Surface in Lens Space
Han Zhang
TL;DR
This paper introduces a method to construct rational Seifert surfaces for knots in Lens spaces using projections on Heegaard tori, expanding tools for knot theory in 3-manifolds.
Contribution
It provides a new construction technique for rational Seifert surfaces in Lens spaces based on knot projections on Heegaard tori.
Findings
Constructs rational Seifert surfaces from knot projections on Heegaard tori.
Applicable to both smooth and piecewise linear knots in Lens spaces.
Offers a systematic approach for analyzing knots in 3-manifolds.
Abstract
In this note, I give a method to construct rational Seifert surface for those smooth or piece-wise linear oriented knots in Lens space. I assume that the oriented knot has a regular projection on Heegaard torus and then construct rational Seifert surface on twist toroidal diagram.
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Taxonomy
TopicsGeometric and Algebraic Topology