Q:Information: - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space. Analogous to how an ordinary sphere (or 2-sphere) is a two-dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms the boundary of a ball in four dimensions. A 3-sphere is an example of a 3-manifold. - 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. - Peter B. Shalen (born c. 1944) is an American mathematician, working primarily in low-dimensional topology. He is the "S" in JSJ decomposition. - 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. - The University of Texas at Austin, informally UT Austin, UT, University of Texas, or Texas in sports contexts, is a public research university and the flagship institution of the University of Texas System. Founded in 1881 as "The University of Texas," its campus is in Austin, Texasapproximately from the Texas State Capitol. The institution has the nation's seventh-largest single-campus enrollment, with over 50,000 undergraduate and graduate students and over 24,000 faculty and staff. - 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, low-dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. It can be regarded as a part of geometric topology. - 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. - Education is the process of facilitating learning, or the acquisition of knowledge, skills, values, beliefs, and habits. Educational methods include storytelling, discussion, teaching, training, and directed research. Education frequently takes place under the guidance of educators, but learners may also educate themselves. Education can take place in formal or informal settings and any experience that has a formative effect on the way one thinks, feels, or acts may be considered educational. The methodology of teaching is called pedagogy. - Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. - Expert is defined differently in varying academic fields. Psychology defines an expert using superior performance; sociology considers that expertise is a label given to an individual by a group and is interested in the power held by experts; philosophy stresses the kind of knowledge held by experts but not novices. Informally, an expert is someone widely recognized as a reliable source of technique or skill whose faculty for judging or deciding rightly, justly, or wisely is accorded authority and status by peers or the public in a specific well-distinguished domain. An expert, more generally, is a person with extensive knowledge or ability based on research, experience, or occupation and in a particular area of study. Experts are called in for advice on their respective subject, but they do not always agree on the particulars of a field of study. An expert can be believed, by virtue of credential, training, education, profession, publication or experience, to have special knowledge of a subject beyond that of the average person, sufficient that others may officially (and legally) rely upon the individual's opinion. Historically, an expert was referred to as a sage (Sophos). The individual was usually a profound thinker distinguished for wisdom and sound judgment. - Latin (Latin: ) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets. - In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are smooth. - Austin is the capital of the U.S. state of Texas and the seat of Travis County. It is the city in the U.S. and the in Texas. It is the fastest growing city in the United States and the second most populated capital city after Phoenix, Arizona. As of the U.S. Census Bureau's July 1, 2015 estimate, Austin has a population of 931,830. Located in in the foothills of Texas Hill Country, the city is home to numerous lakes, rivers, and waterways including Lady Bird Lake, Barton Springs, McKinney Falls, the Colorado River, Lake Travis, and Lake Walter E. Long. It is the cultural and economic center of the metropolitan area, which had an estimated population of 2,064,149 as of June 1, 2016. - 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. - In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: - Cameron Gordon ( born 1945 ) is a Professor and Sid W. Richardson Foundation Regents Chair in the Department of mathematics at the University of Texas at Austin , known for his work in knot theory . Among his notable results is his work with Marc Culler , John Luecke , and Peter Shalen on the cyclic surgery theorem . This was an important ingredient in his work with Luecke showing that knots were determined by their complement . Gordon was also involved in the resolution of the Smith conjecture . Andrew Casson and Gordon defined and proved basic theorems regarding strongly irreducible Heegaard splittings , an important concept in the modernization of Heegaard splitting theory . They also worked on the slice - ribbon conjecture , inventing the Casson - Gordon invariants in the process . Gordon was a 1999 Guggenheim Fellow . In 2005 Gordon was elected a Corresponding Fellow of the Royal Society of Edinburgh . - 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. - In mathematics, the Smith conjecture states that if "f" is a diffeomorphism of the 3-sphere of finite order, then the fixed point set of "f" cannot be a nontrivial knot. - 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 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. - The Texas State Capitol, completed in 1888 in Downtown Austin, contains the offices and chambers of the Texas Legislature and the Office of the Governor. Designed in 1881 by architect Elijah E. Myers, it was constructed from 1882 to 1888 under the direction of civil engineer Reuben Lindsay Walker. A $75 million underground extension was completed in 1993. The building was added to the National Register of Historic Places in 1970 and recognized as a National Historic Landmark in 1986. The Texas State Capitol is tall, making it the sixth tallest state capitol and one of several taller than the United States Capitol in Washington, D.C. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - 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. - The University of Texas System (UT System) encompasses 14 educational institutions in the U.S. state of Texas, of which eight are academic universities and six are health institutions. The UTSystem is headquartered in Austin, and has a total enrollment of over 216,000 students (largest university system in Texas) and employs more than 87,000 faculty and staff. The UT System's $36 billion endowment (as of May 31, 2016) is the largest of any public university system in the United States. Given the information above, choose from the list below the object entity that exhibits the relation 'field of work' with the subject 'cameron gordon '. Choices: - bird - education - engineer - geometry - health - knot theory - language - map - mathematician - mathematics - physics - psychology - research - science - topology - training
A:
topology