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Recent changes: Intersection form Homology groups (simplicial; simple definition) Embeddings just below the stable range: classification 3-manifolds in 6-space Embeddings in Euclidean space: an introduction to their classification Intersection number of immersions High codimension links Embeddings of k-complexes in 2k-manifolds and minimum rank of partial symmetric matrices Knots, i.e. embeddings of spheres Embeddings of manifolds with boundary: classification

Welcome to the Manifold Atlas Project
sponsored by the Hausdorff Center for Mathematics

The Manifold Atlas is a scientific wiki designed for researchers and students interested in manifolds. There are six chapters.

• Manifolds: with pages about constructions and examples of manifolds as well as their invariants and properties.
• Theory: with pages summarising useful general facts and theorems.
• Problems: with pages listing persistent and deep open problems, their status and their history.
• History: with pages about the history of the study of manifolds.
• Philosophy: with pages on the philosophy of mathematics as it relates to manifolds.
• Questions: with pages containing questions and answers about any aspect of the study of manifolds.

You will find the pages listed alphabetically by clicking each chapter.

Evolving pages are the Atlas' work space: they offer a context for collaboratively organising and creating knowledge about manifolds.

Static pages will be scientifically citable: they will have been refereed and then finally approved by the editorial board.

General information

• The Manifold Atlas is hosted by the Hausdorff Institute for Mathematics.
• For more information please follow these links: about the Atlas, the Atlas diary and the editorial board.
• A quick index of pages with additional information is found on the Tools page.

Using the Manifold Atlas

The page User orientation gives information for registered users.

The page Author orientation gives information about writing in the Atlas.

• Join the discussion about a page.
• Add to or edit existing open-editing articles.
• Create a new open-editing page.
• Create a new author-based page.

Registering for the Manifold Atlas

• Please register with a verified email address in order to write and discuss in the Manifold Atlas.

• To sign up for email up-dates about changes at the Atlas visit the Atlas Observer.