Some spaces of polynomial knots
Hitesh Raundal, Rama Mishra

TL;DR
This paper investigates the topology of spaces of polynomial knots, revealing their homotopy types, connectivity, and relationships between different spaces, with implications for knot classification.
Contribution
It establishes the homotopy type of polynomial knot spaces and their connectivity properties, providing new insights into their topological structure.
Findings
Spaces and are path connected for d3
Space has the same homotopy type as S^2
Number of path components in are multiples of eight
Abstract
In this paper we study the topology of three different kinds of spaces associated to polynomial knots of degree at most , for . We denote these spaces by , and . For , we show that the spaces and are path connected and the space has the same homotopy type as . Considering the space of all polynomial knots with the inductive limit topology, we prove that it too has the same homotopy type as . We also show that if two polynomial knots are path equivalent in , then they are topologically equivalent. Furthermore, the number of path components in are in multiples of eight.
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.
