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Erik Christopher Zeeman
Sir Erik Christopher Zeeman FRS (4 February 1925 – 13 February 2016), was a British mathematician, known for his work in geometric topology and singularity theory. Overview Zeeman's main contributions to mathematics were in topology, particularly in knot theory, the piecewise linear category, and dynamical systems. His 1955 thesis at the University of Cambridge described a new theory termed "dihomology", an algebraic structure associated to a topological space, containing both homology and cohomology, introducing what is now known as the Zeeman spectral sequence. This was studied by Clint McCrory in his 1972 Brandeis thesis following a suggestion of Dennis Sullivan that one make "a general study of the Zeeman spectral sequence to see how singularities in a space perturb Poincaré duality". This in turn led to the discovery of intersection homology by Robert MacPherson and Mark Goresky at Brown University where McCrory was appointed in 1974. From 1976 to 1977 he was the Don ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woodstock, Oxfordshire
Woodstock is a market town and civil parish, north-west of Oxford in West Oxfordshire in the county of Oxfordshire, England. The 2011 Census recorded a parish population of 3,100. Blenheim Palace, a UNESCO World Heritage Site, is next to Woodstock, in the parish of Blenheim. Winston Churchill was born in the palace in 1874 and buried in the nearby village of Bladon. Edward, elder son of King Edward III and heir apparent, was born in Woodstock Manor on 15 June 1330. In his lifetime he was commonly called Edward of Woodstock, but is known today as the Black Prince. In the reign of Queen Mary I, her half-sister Elizabeth was imprisoned in the gatehouse of Woodstock Manor. History The name Woodstock is Old English in origin, meaning a "clearing in the woods". The Domesday Book of 1086 describes Woodstock (''Wodestock, Wodestok, Wodestole'') as a royal forest. Æthelred the Unready, king of England, is said to have held an assembly at Woodstock at which he issued a legal code no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeeman Conjecture
In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex K, the space K\times ,1/math> is collapsible. The conjecture, due to Christopher Zeeman, implies the Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured ... and the Andrews–Curtis conjecture. References * Conjectures Unsolved problems in geometry Geometric topology {{topology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piecewise Linear Manifold
In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise linear functions. This is slightly stronger than the topological notion of a triangulation. An isomorphism of PL manifolds is called a PL homeomorphism. Relation to other categories of manifolds PL, or more precisely PDIFF, sits between DIFF (the category of smooth manifolds) and TOP (the category of topological manifolds): it is categorically "better behaved" than DIFF — for example, the Generalized Poincaré conjecture is true in PL (with the possible exception of dimension 4, where it is equivalent to DIFF), but is false generally in DIFF — but is "worse behaved" than TOP, as elaborated in surgery theory. Smooth manifolds Smooth manifolds have canonical PL structures — they are uniquely ''triangulizable,'' by Whitehead's theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, Unknot, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not 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 \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singularity Theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined "U". This is another kind of singularity. Unlike the double point, it is not ''stable'', in the sense that a small push will lift the bottom of the "U" away from the "underline". Vladimir Arnold defines the main goal of singularity theory as describing how objects depend on parameters, particularly in cases where the properties undergo sudden change under a small variation of the parameters. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originated in the 1935 classification of lens spaces by Reidemeister torsion, which required distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of ''simple'' homotopy theory. The use of the term geometric topology to describe these seems to have originated rather recently. Differences between low-dimensional and high-dimensional topology Manifolds differ radically in behavior in high and low dimension. High-dimensional topology refers to manifolds of dimension 5 and above, or in relative terms, embeddings in codimension 3 and above. Low-dimensional topology is concerned with questions in dimensions up to 4, or embeddings in codimension up to 2. Dimension 4 is special, in that in some respects (topologica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford Times
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the University of Oxford, the oldest university in the English-speaking world; it has buildings in every style of English architecture since late Anglo-Saxon. Oxford's industries include motor manufacturing, education, publishing, information technology and science. History The history of Oxford in England dates back to its original settlement in the Saxon period. Originally of strategic significance due to its controlling location on the upper reaches of the River Thames at its junction with the River Cherwell, the town grew in national importance during the early Norman period, and in the late 12th century became home to the fledgling University of Oxford. The city was besieged during The Anarchy in 1142. The university rose to domin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, including mathematics, engineering science, and medical science". Fellow, Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to many eminent scientists throughout history, including Isaac Newton (1672), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Albert Einstein (1921), Paul Dirac (1930), Winston Churchill (1941), Subrahmanyan Chandrasekhar (1944), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955) and Francis Crick (1959). More recently, fellowship has been awarded to Stephen Hawking (1974), David Attenborough (1983), Tim Hunt (1991), Elizabeth Blackburn (1992), Tim Berners-Lee (2001), Venki R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
:Category:David Crighton Medalists
The Institute of Mathematics and its Applications and the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ... instituted the David Crighton Medal in 2002. {{DEFAULTSORT:Crighton, David, medalists Awards of the London Mathematical Society Mathematicians by award Science and technology award winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Faraday Prize
The Royal Society of London Michael Faraday Prize is awarded for "excellence in communicating science to UK audiences". Named after Michael Faraday, the medal itself is made of silver gilt, and is accompanied by a purse of £2500. Background The prize was first awarded in 1986 to Charles Taylor for "his outstanding presentations of physics and applications of physics, aimed at audiences from six-year-old primary school children to adults". It is awarded annually and unlike other Royal Society awards such as the Hughes Medal, it has been presented every year since its inception. The winner is required to present a lecture as part of the Society's annual programme of public events, which is usually held in January of the following year; during the lecture, the President of the Royal Society awards the medal. Unlike other prizes awarded by the society, the committee has not always publicly provided a rationale. This has occurred five times—in 2004 to Martin Rees, in 2006 to Richa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
