self-homeomorphism
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Homeomorphism — Topological equivalence redirects here; see also topological equivalence (dynamical systems). donut illustrating that they are homeomorphic. But there does not need to be a continuous deformation for two spaces to be homeomorphic.In the… … Wikipedia
Self-similarity — NOTOC [ thumb|right|250px|A Koch curve has an infinitely repeating self similarity when it is magnified.] In mathematics, a self similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or… … Wikipedia
Gordon-Luecke theorem — In mathematics, the Gordon Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… … Wikipedia
Gordon–Luecke theorem — In mathematics, the Gordon–Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… … Wikipedia
Chiral knot — In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image. An oriented knot that is equivalent to its mirror image is an amphichiral knot, also called an achiral knot or amphicheiral knot. The… … Wikipedia
Automorphism — In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms… … Wikipedia
Mapping torus — In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components… … Wikipedia
Knot group — In mathematics, a knot is an embedding of a circle into 3 dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,:pi 1(mathbb{R}^3 ackslash K).Two equivalent knots have… … Wikipedia
Modular group — For a group whose lattice of subgroups is modular see Iwasawa group. In mathematics, the modular group Γ is a fundamental object of study in number theory, geometry, algebra, and many other areas of advanced mathematics. The modular group can be… … Wikipedia
Dehn twist — A positive Dehn twist applied to a cylinder about the red curve c modifies the green curve as shown. In geometric topology, a branch of mathematics, a Dehn twist is a certain type of self homeomorphism of a surface (two dimensional manifold).… … Wikipedia
Ambient isotopy — In the mathematical subject of topology, an ambient isotopy, also called an h isotopy, is a kind of continuous distortion of an ambient space , a manifold, taking a submanifold to another submanifold. For example in knot theory, one considers two … Wikipedia
