Related Research Articles
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its diffeomorphism group. Because many of these coarser properties may be captured algebraically, differential topology has strong links to algebraic topology.
William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface can be given one of three geometries . In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by William Thurston, and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture.
In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.
In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of continuum theory.
Mikhael Leonidovich Gromov is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of Institut des Hautes Études Scientifiques in France and a professor of mathematics at New York University.
In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to −1. It is generally required that this metric be also complete: in this case the manifold can be realised as a quotient of the 3-dimensional hyperbolic space by a discrete group of isometries.
In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by Jakob Nielsen.
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction". Anosov systems are a special case of Axiom A systems.
In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations.
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, specifically geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence should imply a stronger, topological notion.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University.
John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.
In geometry, Thurston's geometrization theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular satisfy the Thurston conjecture.
The Geometry Festival is an annual mathematics conference held in the United States.
Wolfgang Lück is a German mathematician who is an internationally recognized expert in algebraic topology.
Francis Thomas Farrell is an American mathematician who has made contributions in the area of topology and differential geometry. Farrell is a distinguished professor emeritus of mathematics at Binghamton University. He also holds a position at the Yau Mathematical Sciences Center, Tsinghua University.
Wu-Chung Hsiang is a Taiwanese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.
Pedro Ontaneda Portal is a Peruvian-American mathematician specializing in topology. He is a distinguished professor at Binghamton University, a unit of the State University of New York. He received his Ph.D. in 1994 from Stony Brook University, advised by Lowell Jones; subsequently he taught at the Federal University of Pernambuco in Brazil before moving to Binghamton.
References
- ↑ "Stony Brook Faculty page" . Retrieved 20 December 2015.
- ↑ Lowell E. Jones at the Mathematics Genealogy Project
- ↑ Jones, Lowell (1972). "The converse to the fixed point theorem of P. A. Smith" (PDF). Bulletin of the American Mathematical Society . 78 (2): 234–236. doi: 10.1090/S0002-9904-1972-12934-3 . JSTOR 1970734.
- ↑ Farrell, F. Thomas; Jones, Lowell E. (1978). "Anosov diffeomorphisms constructed from π1 Diff (Sn)". Topology . 17 (3): 273–282. doi: 10.1016/0040-9383(78)90031-9 .
- ↑ Farrell, F. Thomas; Jones, Lowell E. (Apr 1993). "Isomorphism Conjectures in Algebraic K-Theory". Journal of the American Mathematical Society . 2 (6): 249–297. doi:10.2307/2152801. JSTOR 2152801.
- ↑ Davis, James (2012). "The Work of Tom Farrell and Lowell Jones in Topology and Geometry". Pure and Applied Mathematics Quarterly. 8 (1): 1–14. arXiv: 1006.1489 . Bibcode:2010arXiv1006.1489D. doi:10.4310/PAMQ.2012.v8.n1.a3. S2CID 55560396.
- ↑ "Speakers at the ICM" . Retrieved 21 December 2015.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
   | This article about an American mathematician is a stub. You can help Wikipedia by expanding it. |