query: field_of_work morwen thistlethwaite
supports: 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 knots the same if one can distort one knot into the other without breaking it. Such a distortion is an example of an ambient isotopy. More precisely, let "N" and "M" be manifolds and "g" and "h" be embeddings of "N" in "M". A continuous map 
  is defined to be an ambient isotopy taking "g" to "h" if "F" is the identity map, each map "F" is a homeomorphism from "M" to itself, and "F"  "g" = "h". This implies that the orientation must be preserved by ambient isotopies. For example, two knots which are mirror images of each other are in general not equivalent. Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ern Rubik.
  Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer, and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide making it the world's top-selling puzzle game. It is widely considered to be the world's best-selling toy. A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. Professor (commonly abbreviated as "prof.") is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, "professor" derives from Latin as a "person who professes" being usually an expert in arts or sciences, a teacher of the highest rank. In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spacesthat is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word "homeomorphism" comes from the Greek words "" ("homoios") = similar and "" ("morph") = shape, form. Morwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville . He has made important contributions to both knot theory and Rubik 's Cube group theory . In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R (in topology, a circle isn't bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself. In mathematics, topology (from the Greek , "place", and , "study") is concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important topological properties include connectedness and compactness. In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions. Architecture (Latin "architectura", from the Greek  "arkhitekton" "architect", from - "chief" and  "builder") is both the process and the product of planning, designing, and constructing buildings and other physical structures. Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art. Historical civilizations are often identified with their surviving architectural achievements. Ern Rubik (born 13 July 1944) is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including Rubik's Cube (1974), Rubik's Magic, , and Rubik's Snake.
candidates: architecture art education geometry invention knot theory mathematics physics research topology
answer: topology