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: mafinar
The following languages will help current and new web developers navigate the programming landscape to code web-based services and apps t...
New
CommunityNews
ABSTRACT In lieu of a traditional , I’ve tried to distill the essence of the talk into a collection of maxims: All programmers are API ...
New
First poster: bot
Apple’s Tim Cook to take 50% pay hit after shareholder feedback. ‘Target compensation’ for CEO down from $99.4m in 2022 to an expected $...
New
First poster: mikhailgrib
Let’s build GPT: from scratch, in code, spelled out… We build a Generatively Pretrained Transformer (GPT), following the paper “Attentio...
New
First poster: bot
Hector Martin (@marcan@treehouse.systems). Attached: 1 image For those wondering why the hell we need all this safety system stuff for...
New
First poster: FatimaAdamu
Two US lawyers fined for submitting fake court citations from ChatGPT. Law firm also penalised after chatbot invented six legal cases th...
New
CommunityNews
Apple Patents Suggest Future AirPods Could Monitor Biosignals & Brain Activity - AppleMagazine. The US Patent & Trademark Office...
New
First poster: fullstackplus
Why Python is terrible… Nice language, but unsuitable for most professional purposes
New
First poster: alvinkatojr
There are countless articles why developers should not focus on Frameworks too much and instead learn to understand the underlying langua...
New
New

Other popular topics Top

PragmaticBookshelf
Stop developing web apps with yesterday’s tools. Today, developers are increasingly adopting Clojure as a web-development platform. See f...
New
AstonJ
poll poll Be sure to check out @Dusty’s article posted here: An Introduction to Alternative Keyboard Layouts It’s one of the best write-...
New
AstonJ
I ended up cancelling my Moonlander order as I think it’s just going to be a bit too bulky for me. I think the Planck and the Preonic (o...
New
PragmaticBookshelf
Learn different ways of writing concurrent code in Elixir and increase your application's performance, without sacrificing scalability or...
New
PragmaticBookshelf
Use WebRTC to build web applications that stream media and data in real time directly from one user to another, all in the browser. ...
New
PragmaticBookshelf
Get the comprehensive, insider information you need for Rails 8 with the new edition of this award-winning classic. Sam Ruby @rubys ...
New
AnfaengerAlex
Hello, I’m a beginner in Android development and I’m facing an issue with my project setup. In my build.gradle.kts file, I have the foll...
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
RobertRichards
Hair Salon Games for Girls Fun Girls Hair Saloon game is mainly developed for kids. This game allows users to select virtual avatars to ...
New
PragmaticBookshelf
Fight complexity and reclaim the original spirit of agility by learning to simplify how you develop software. The result: a more humane a...
New