40 citations · 186 across the 33 of their papers we have counts for
28 papers · 1 filter
Gordian Unlinks
José Ayala, Joel Hass
This paper gives the first examples of gordian unlinks. The components of these unlinks cannot be separated while maintaining constant length and thickness. We construct infinite f…
Random Colorings in Manifolds
Chaim Even-Zohar, Joel Hass
We develop a general method for constructing random manifolds and submanifolds in arbitrary dimensions. The method is based on associating colors to the vertices of a triangulated…
Surfaces and their Profile Curves
Joel Hass
This paper examines the relationship between the knotting of an embedded surface in and the knotting of its fold curves, formed by the singular set of projection to a plane.…
Tangle decompositions of alternating link complements
Joel Hass, Abigail Thompson, Anastasiia Tsvietkova
Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish in [3]; Lickori…
Alternating links have at most polynomially many Seifert surfaces of fixed genus
Joel Hass, Abigail Thompson, Anastasiia Tsvietkova
Let be a non-split prime alternating link with crossings. We show that for each fixed , the number of genus- Seifert surfaces for is bounded by an explicitly gi…
Universal Knot Diagrams
Chaim Even-Zohar, Joel Hass, Nati Linial +1
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implic…