Classification of manifolds information

topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Low-dimensional manifolds are classified...

smooth) manifolds, surgery techniques also apply to piecewise linear (PL-) and topological manifolds. Surgery refers to cutting out parts of the manifold and...

class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are...

Classification of Platonic solids Classification theorems of surfaces Classification of two-dimensional closed manifolds – Two-dimensional manifoldPages...

(e.g. CT scans). Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable...

and Fréchet manifolds, in particular manifolds of mappings are infinite dimensional differentiable manifolds. For a Ck manifold M, the set of real-valued...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner...

Thus the topological classification of 4-manifolds is in principle tractable, and the key questions are: does a topological manifold admit a differentiable...

that require only a smooth structure on a manifold to be defined. Smooth manifolds are 'softer' than manifolds with extra geometric structures, which can...

are versions of the surgery exact sequence depending on the category of manifolds we work with: smooth (DIFF), PL, or topological manifolds and whether...

different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding...

below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Fréchet manifolds, replacing Banach...

un-obstructedness of the deformation space for hyperkaehler manifolds (in 1978 paper) and then extended this to all Calabi–Yau manifolds in the 1981 IHES...

Calabi–Yau manifolds with SU(2) or SU(3) holonomy. Also important are compactifications on G2 manifolds. Computing the holonomy of Riemannian manifolds has been...

physics, the classification of electromagnetic fields is a pointwise classification of bivectors at each point of a Lorentzian manifold. It is used in...

constructing Calabi–Yau manifolds with cylindrical ends, resulting in tens of thousands of diffeomorphism types of new examples. These manifolds are important in...

General topology 55: Algebraic topology 57: Manifolds and cell complexes 58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphy)...

structure of manifolds and fiber bundles are partial functions. In the case of manifolds, the domain is the point set of the manifold. In the case of fiber bundles...

several ways). The complete list of such manifolds is given in the article on spherical 3-manifolds. Under Ricci flow, manifolds with this geometry collapse...