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<wikitex>; The Manifold Atlas emphasises constructions and examples of manifolds. We suggest, but do not insist, that an article in the Manifolds chapter has the following structure: <pre> == Introduction == == Construction and examples == == Invariants == == Classification/Characterization (if available) == == Further discussion == == References == </pre> == Introduction == Briefly orient the reader to manifolds to be discussed: ideally specify the default category being used. This section may be omitted. == Construction and examples == Present the construction(s) of the manifolds of intereset. Following that give examples of manifolds falling under the construction(s). == Invariants == List and where necessary describe invariants of intereset. Where possible, record the known values of these invariants. Here are some simple suggestions for invariants. * (Co)Homology groups and rings. * Homotopy groups. * Euler characteristic. * Characteristic classes. <!-- ** Stiefel-Whitney classes. ** Pontrjagin classes. ** Chern classes.--> * Orientability. == Classification and/or characterisation == * Report what is known concerning completeness of the invariants listed for this class of manifolds or manifold. * Statements here will typically depend upon the category chosen, the more classification results over more diverse categories, the better. == Further topics == These could include * Open problems related to this collection of manifolds: ideally write a [[:Category: Problems|Problems]] page and link to it. * Occurences of the manifolds in or other branches of mathematics. * Existence and properties of further structures. * Curvature and metric properties. * Embedding/immersions into $\Rr^n$. * Mapping class groups. * [[Chirality]]. * Group actions or other interesting self-maps. == Categories == To enable searching for manifolds with given properties, manifolds pages will contain links to [[Special:Categories]]. For example, an article describing an orientable manifold should contain the link <pre> [[Category:orientable]] </pre> at the end of the article. <!--This is of course only a suggestion, and different families of manifolds may require different structures of their articles. --> </wikitex>

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