Manifold Atlas:The definitions project

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This page gives guide lines for authors writing Definitions pages.

1 Scientific aspects

Although definition pages should reflect the individual style of their writers, our aim is that they share a common overarching style. Here are the main points:

1.) The name of your page should be the concept you intend to define; e.g. Fundamental class.

2.) Formulate your definition using succinct and clear language and standard mathematical terminology. Most definitions will not exceed three A4 pages when printed out.

3.) Endeavor to give some examples which help to clarify and illustrate the definition.

4.) If there is a fundamental theorem in which the concept you define plays a key role, clearly state this theorem with a reference to the literature but without proof. Moreover, if there are relevant statements which can be clearly formulated and which clarify the mathematics surrounding the definition, you should consider adding them: in this case it is preferable to give a reference, if this is not possible, a proof should be given.

5.) If in your definition you use another definition which is not contained in standard graduate courses, please check whether the definition is already on the atlas and refer to it. If not, please either write the definition yourself in a separate page or inform the administrator and we will look for somebody to write this definition.

6.) You was wish to consult the published defintions pages on BoMA - Definitions.

In addition, here are two examples on the Manifold Atlas, the first brief, the second more elaborate:

Of course the styles of these pages may not be appropriate for all definitions but the examples indicate the sort of page we are aiming for.

2 Technical aspects

You can either write your definition as a standard TeX file and then email the administrator.

Alternatively, you can use the Wiki system directly. For more information about using the Wiki system, please consult the page Writing in the Atlas.

To get oriented for writing, it is good to know what is already on-line for your topic. For links to relevant Wikipedia pages, Atlas pages, or articles in the Encyclopeadia of Mathematics, please consult the following page on our support Wiki: MAP Definitions

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