Stabilization in the Braid Groups (with applications to transverse knots)

TL;DR

This work investigates stabilization processes within braid groups and explores their implications for the classification and properties of transverse knots, providing foundational insights and tools for knot theory and contact topology.

Contribution

The paper introduces new stabilization techniques in braid groups and applies them to analyze the transverse simplicity of knots, advancing understanding in knot classification.

Findings

Stabilization methods facilitate classification of transverse knots

New criteria for transverse simplicity established

Connections between braid group stabilization and knot invariants

Abstract

Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/0310279, and (2) "Stabilization in the braid groups II: Transversal simplicity of knots", Geometry and Topology Volume 10 (2006), to appear, arXiv:math,GT/0310280.