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:
Popular General Dev topics
A field guide to help you recognize achievement, spot A field guide to help you recognize achievement, spot bottlenecks, and debug your d...
New
TOKYO (Kyodo) – Japan’s government plans to encourage firms to let their employees choose to work four days a week instead of five, aimin...
New
Last night I re-read this Steve Yegge article about learning to type as a programmer. I can touch type, but I don’t usually manage to bre...
New
The File System Access API with Origin Private File System.
WebKit supports new API that makes it possible for web apps to create, open,...
New
LG 28-inch 16:18 DualUp Monitor with Ergo Stand and USB Type-C™ (28MQ780-B) | LG USA.
Shop LG 28MQ780-B on the official LG.com website ...
New
GitHub - crablang/crab: A community fork of a language named after a plant fungus. All of the memory-safe features you love, now with 100...
New
Apple Patents Suggest Future AirPods Could Monitor Biosignals & Brain Activity - AppleMagazine.
The US Patent & Trademark Office...
New
SLUM: The Shadow Library Uptime Monitor.
This dashboard tracks the availability of popular shadow libraries in real time from a US-based...
New
To avoid being replaced by LLMs, do what they can’t.
What LLM’s can’t do yet
New
In beginning the NVIDIA Blackwell Linux testing with the GeForce RTX 5090 compute performance, besides all the CUDA/OpenCL/OptiX benchmar...
New
Other popular topics
No chair. I have a standing desk.
This post was split into a dedicated thread from our thread about chairs :slight_smile:
New
New
Small essay with thoughts on macOS vs. Linux:
I know @Exadra37 is just waiting around the corner to scream at me “I TOLD YOU SO!!!” but I...
New
Tailwind CSS is an exciting new CSS framework that allows you to design your site by composing simple utility classes to create complex e...
New
Build highly interactive applications without ever leaving Elixir, the way the experts do. Let LiveView take care of performance, scalabi...
New
Intensively researching Erlang books and additional resources on it, I have found that the topic of using Regular Expressions is either c...
New
If you want a quick and easy way to block any website on your Mac using Little Snitch simply…
File > New Rule:
And select Deny, O...
New
Author Spotlight
Erin Dees
@undees
Welcome to our new author spotlight! We had the pleasure of chatting with Erin Dees, co-author of ...
New
Get the comprehensive, insider information you need for Rails 8 with the new edition of this award-winning classic.
Sam Ruby @rubys
...
New
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
Categories:
Sub Categories:
- All
- In The News
- Dev Chat (202)
- Questions (34)
- Resources (119)
- Blogs/Talks (27)
- Jobs (3)
- Events (15)
- Code Editors (59)
- Hardware (57)
- Reviews (5)
- Sales (16)
- Design & UX (5)
- Marketing & SEO (2)
- Industry & Culture (14)
- Ethics & Privacy (19)
- Business (4)
- Learning Methods (5)
- Content Creators (7)
- DevOps & Hosting (9)
Popular Portals
- /elixir
- /rust
- /ruby
- /wasm
- /erlang
- /phoenix
- /keyboards
- /rails
- /python
- /js
- /security
- /go
- /swift
- /vim
- /clojure
- /emacs
- /haskell
- /java
- /svelte
- /onivim
- /typescript
- /kotlin
- /c-plus-plus
- /crystal
- /tailwind
- /react
- /gleam
- /ocaml
- /flutter
- /elm
- /vscode
- /ash
- /opensuse
- /html
- /centos
- /php
- /deepseek
- /zig
- /scala
- /sublime-text
- /lisp
- /textmate
- /react-native
- /nixos
- /debian
- /agda
- /kubuntu
- /arch-linux
- /django
- /revery
- /ubuntu
- /manjaro
- /deno
- /spring
- /nodejs
- /diversity
- /lua
- /julia
- /slackware
- /c






