CommunityNews

CommunityNews

A Fast, Strong, Topologically Meaningful and Fun Knot Invariant

In this paper we discuss a pair of polynomial knot invariants $Θ=(Δ,θ)$ which is:

  • Theoretically and practically fast: $Θ$ can be computed in polynomial time. We can compute it in full on random knots with over 300 crossings, and its evaluation at simple rational numbers on random knots with over 600 crossings.
  • Strong: Its separation power is much greater than the hyperbolic volume, the HOMFLY-PT polynomial and Khovanov homology (taken together) on knots with up to 15 crossings (while being computable on much larger knots).
  • Topologically meaningful: It likely gives a genus bound, and there are reasons to hope that it would do more.
  • Fun: Scroll to Figures 1.1-1.4, 3.1, and 6.2.
    $Δ$ is merely the Alexander polynomial. $θ$ is almost certainly equal to an invariant that was studied extensively by Ohtsuki, continuing Rozansky, Kricker, and Garoufalidis. Yet our formulas, proofs, and programs are much simpler and enable its computation even on very large knots.

Read in full here:

Where Next?

Popular General Dev topics Top

First poster: malloryerik
GitHub - hlissner/doom-emacs: An Emacs framework for the stubborn martian hacker. An Emacs framework for the stubborn martian hacker - G...
New
OvermindDL1
Yet another rust-made text editor, though I’m really liking the looks of how this one works!
New
First poster: bot
API Gateway Trends behind Features: Apache APISIX 3.0 vs. Kong 3.0 - API7.ai. By comparing the open-source API Gateway Apache APISIX and...
New
First poster: peterchancc
Why I like Clojure as a solo developer | Biff. Most of the reasons fall into a few categories: data orientation, the JVM, and the REPL.
New
CommunityNews
The Definitive PHP 7.2, 7.3, 7.4, 8.0, and 8.1 Benchmarks (2023). We tested the performance of 14 PHP platforms (WordPress, Drupal, Lara...
New
First poster: AstonJ
Jan | Rethink the Computer. Jan turns your computer into an AI machine by running LLMs locally on your computer. It’s a privacy-focus, l...
New
First poster: DevotionGeo
To avoid being replaced by LLMs, do what they can’t. What LLM’s can’t do yet
New
First poster: chris.johan
Skype’s days appear to be numbered, as a hidden string in the latest Skype for Windows preview suggests Microsoft will shutter the servic...
New
New
First poster: jss
Bare is a minimal and modular JavaScript runtime designed for building high-performance apps across desktop and mobile. Open-source, fast...
New

Other popular topics Top

Devtalk
Hello Devtalk World! Please let us know a little about who you are and where you’re from :nerd_face:
New
New
AstonJ
Do the test and post your score :nerd_face: :keyboard: If possible, please add info such as the keyboard you’re using, the layout (Qw...
New
mafinar
This is going to be a long an frequently posted thread. While talking to a friend of mine who has taken data structure and algorithm cou...
New
PragmaticBookshelf
Author Spotlight Jamis Buck @jamis This month, we have the pleasure of spotlighting author Jamis Buck, who has written Mazes for Prog...
New
PragmaticBookshelf
Develop, deploy, and debug BEAM applications using BEAMOps: a new paradigm that focuses on scalability, fault tolerance, and owning each ...
New
AstonJ
This is cool! DEEPSEEK-V3 ON M4 MAC: BLAZING FAST INFERENCE ON APPLE SILICON We just witnessed something incredible: the largest open-s...
New
AstonJ
This is a very quick guide, you just need to: Download LM Studio: https://lmstudio.ai/ Click on search Type DeepSeek, then select the o...
New
NewsBot
Node.js v22.14.0 has been released. Link: Release 2025-02-11, Version 22.14.0 'Jod' (LTS), @aduh95 · nodejs/node · GitHub
New
PragmaticBookshelf
A concise guide to MySQL 9 database administration, covering fundamental concepts, techniques, and best practices. Neil Smyth MySQL...
New