A Temperley-Lieb category for 2-manifolds
Marcos Alvarez, Paul P. Martin
TL;DR
This paper introduces new categories generalizing the Temperley-Lieb category, motivated by lattice model computations in 2 and 3 dimensions, with practical combinatorial methods for their use.
Contribution
It defines novel categories extending Temperley-Lieb, establishes functors to the partition category, and provides combinatorial tools for topological computations.
Findings
New categories generalizing Temperley-Lieb are constructed.
Practical combinatorial methods for computations in these categories are developed.
Connections to lattice model problems in 2 and 3 dimensions are established.
Abstract
Guided by consideration of problems in 2 and 3 dimensional lattice model computation, we are led to define a number of new categories, and functors between these categories and the partition category, culminating in the introduction of two categories generalising the Temperley-Lieb category. We show how to compute practically in these categories, by giving a combinatorial realisation of their (topological) construction.
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
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology