Geometric topology - Citizendia

For other uses, see Geometric topology (disambiguation).

In mathematics, geometric topology is the study of manifolds and their embeddings. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In Mathematics, an embedding (or imbedding) is one instance of some Mathematical structure contained within another instance such as a group Low-dimensional topology, concerning questions of dimensions up to four, is a part of geometric topology. In Mathematics, low-dimensional topology is the branch of Topology that studies Manifolds of four or fewer dimensions

Some examples of topics in geometric topology are orientability, handle decompositions, local flatness, and the planar and higher-dimensional Schönflies theorems. A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back In Mathematics, a handle decomposition of an n - Manifold M is a representation of that manifold as an exhaustion M_0 \subset In Topology, a branch of Mathematics, local flatness is a property of a submanifold in a Topological manifold of larger Dimension. In Mathematics, the Jordan–Schönflies theorem, or simply the Schönflies theorem, of Geometric topology is a sharpening of the Jordan curve theorem

Knot theory is the study of the 3-dimensional embeddings of circles. In Mathematics, knot theory is the area of Topology that studies mathematical knots While inspired by knots which appear in daily life in shoelaces Three-dimensional space is a geometric model of the physical Universe in which we live In Mathematics, an embedding (or imbedding) is one instance of some Mathematical structure contained within another instance such as a group Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the

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