New invariants of Legendrian knots
Noboru Ito, Masashi Takamura
TL;DR
This paper introduces new integer-valued linear invariants for Legendrian knots derived from their front projections, extending the classical Arnold basic invariant for plane curves.
Contribution
It presents novel functions of Legendrian knots that generalize and extend Arnold's basic invariant, offering new tools for knot classification.
Findings
Defined new Legendrian invariants from front projections
Extended Arnold's basic invariant to Legendrian knots
Provided a framework for further generalizations
Abstract
We give new functions of Legendrian knots derived from Legendrian fronts. These are integer-valued linear functions that are alike the Arnold basic invariant of plane curves. Various generalizations of the Arnold basic invariant have been known. In this paper, we give another extension of Arnold's idea.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Advanced Numerical Analysis Techniques