TL;DR
This paper investigates the conditions under which homogeneous quasipositive links are positive, demonstrating that certain diagrams with equal Seifert circles and braid index are necessarily positive.
Contribution
It establishes a criterion linking homogeneous quasipositive links and positive diagrams based on Seifert circles and braid index.
Findings
Homogeneous quasipositive links can be positive under specific diagram conditions.
A homogeneous diagram with equal Seifert circles and braid index is positive.
The paper provides a criterion for positivity in quasipositive links.
Abstract
We discuss when homogeneous quasipositive links are positive. In particular, we show that a homogeneous diagram of a quasipositive link whose number of Seifert circles is equal to the braid index is a positive diagram.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows