Diffgeom:Purpose statement

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This article is about the diffgeom wiki itself

This page describes what the basic purpose of diffgeom is. It is written by Vipul Naik, the person currently running the wiki.

The motivation behind diffgeom

Diffgeom has been started on an experimental basis to mimic many of the successful features of the Group properties wiki. By successful is meant features on the Group properties wiki that seem to make for systematic and powerful documentation. In particular, Diffgeom hopes to be an active repository of definitions, facts, proofs and motivational material in the theory of differential manifolds, Riemannian manifolds, differential topology, symplectic/contact geometry, and related subjects. Diffgeom aims to be:

  • A quick reference tool for gathering the basic definition and important properties of any term/concept
  • A quick tool to check whether a particular fact (in differential geometry) is true, and to find facts related to a particular term
  • A quick tool to understand the proof of a result and figure out whether that proof is applicable in other contexts
  • A place where one can read articles motivating the development of any term or concept, as well as survey articles explaining the application of a principle or idea or related cluster of ideas

Diffgeom vis-a-vis other reference tools

Diffgeom versus Groupprops

Diffgeom is very much inspired by the Groupprops effort, but it seeks to be different in a number of ways. First of all it does not work on the same organizational principles as Groupprops. For instance, the property-theoretic scheme of classification works very well in group theory, but is not likely to work so well in differential geometry (because of the more continuous nature of differential geometry). So while we do make use of the property-theoretic paradigm we also use a number of other organizational principles and paradigms

Diffgeom versus Wikipedia

Wikipedia is currently one big huge place where you can get everything -- and currently, of course the Wikipedia articles on differential geometry will be far more comprehensive, informative and well-written than those on Diffgeom. However, there are a number of niches where Diffgeom can and will overtake Wikipedia, or for that matter, any general-purpose encyclopaedia. If it is not clear how this is going to happen, check out Groupprops versus Wikipedia for a comparison between a small-scale enterprise like this one, and something huge like Wikipedia.

Diffgeom versus other reference tools

We are currently too small to comment, but hopefully there will be something to say here after some time!