Tropical Ptolemy Transformations and Invariants of Braids
Gurnoor Singh
TL;DR
This paper introduces a novel approach using tropical Ptolemy transformations to construct invariants of braids, linking different mathematical areas through a unified equation.
Contribution
It presents the first application of tropical Ptolemy equations to braid invariants, bridging low-dimensional topology and tropical geometry.
Findings
Tropical Ptolemy equations can be used to define braid invariants.
The approach unifies different mathematical perspectives on the pentagon identity.
New invariants provide potential tools for classifying braids.
Abstract
It often happens in mathematics that one and the same equation is known under different names in different areas of mathematics. The famous pentagon identity appears in low-dimensional topology in different ways. In this paper, we use the tropical version of the Ptolemy equation to construct invariants of braids.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHistorical Astronomy and Related Studies · History and Theory of Mathematics · Ancient Egypt and Archaeology