Groupprops:Groupprops versus Diffgeom

This is an article comparing the Groupprops wiki against:The Differential Geometry Wiki

A number of new wikis have been started off on the pattern of Groupprops. None of them has yet reached the pre-alpha stage at which Groupprops currently is, and most of them are still finding their way. Relatively among them, the The Differential Geometry Wiki (called Diffgeom) is among the most advanced. Here, I look at the similarities and differencies between Groupprops and Diffgeom.

Group theory versus Differential Geometry

Perhaps the fundamental difference between the two wikis is in the topics they cover! Groupprops is about the theory of groups and related areas, while Diffgeom is about differential geometry and related disciplines like Riemannian geometry and differential topology. Roughly, group theory is very discrete, while differential geometry, by its nature, is continuous, smooth, and geometric. Hence, the kind of policies for categorization, article-tagging, etc. differ quite a bit.

Group theory is probably the area where the property-theoretic paradigm (that is, the paradigm of having a collection of objects and properties over that collection) works best. In differential geometry, because we are working in the continuous setting, simply putting True/False properties doesn't always capture the structure. We also need to deal with real-valued function, that actually measure how much rather than whether or not.

The same article could differ in the two wikis

So far, there are not too many articles of the same name, or on the same topic, that occur in both wikis. Here are some that do occur on both wikis. Compare group (on groupprops) with group (on diffgeom). The notion of group is central to group theory (as the name might suggest), and the article on group in groupprops is developed in a manner that accounts for that centrality. On the other hand, the article on group in the differential geometry wiki is more of a formality.

Another difference is in sections like Importance and Properties, the facts important enough to mention in each section depend on the wiki.

In general, if an article on Groupprops, also has a Diffgeom version, this will be stated either at the top of the article (if the topic is closely related to differential geometry) and/or in the Definition links subsection at the bottom of the article. One can also access a list of articles on Groupprops with Diffgeom versions at:

The user lists and communities differ

The user list communities for both wikis differ; the community which determines the organizational principles and paradigms also differs. This is natural since the organizational principles are themselves different.