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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 ... [...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 Fellows 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". Overview Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to :Fellows of the Royal Society, around 8,000 fellows, including eminent scientists Isaac Newton (1672), Benjamin Franklin (1756), Charles Babbage (1816), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Jagadish Chandra Bose (1920), Albert Einstein (1921), Paul Dirac (1930), Subrahmanyan Chandrasekhar (1944), Prasanta Chandra Mahalanobis (1945), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955), Satyendra Nath Bose (1958), and Francis Crick (1959). More recently, fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, 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, ''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. Dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piecewise Linear Manifold
In mathematics, a piecewise linear manifold (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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In 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, 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. 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 it 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 describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics 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, Torsion (mechanics), 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 List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, 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 to ... [...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. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, 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, ''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. Dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford Times
''The Oxford Times'' is a weekly newspaper, published each Thursday in Oxford, England. The paper is published from a large production facility at Osney Mead, west Oxford, and is owned by Newsquest, the UK subsidiary of US-based Gannett Company. ''The Oxford Times'' has a number of colour supplements. ''Oxfordshire Limited Edition'' is included with the first edition of each month. There is also a monthly ''In Business'' supplement. ''The Oxford Times'' has several sister publications: *''The Herald Series'' – a set of weekly newspapers covering Abingdon, Wantage, Wallingford and Didcot. *''Witney Gazette'' – a weekly newspaper covering Witney and Carterton. *''Bicester Advertiser'' – a weekly newspaper covering Bicester. *''Banbury Cake'' – a free weekly newspaper for the Banbury area. *''Oxford Star'' – a free weekly newspaper which ran from 1976 to 2013. *''Oxford Mail'' – a daily newspaper published Monday to Saturday founded in 1928. History ''The Oxford ... [...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 society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ... 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 Michael Faraday Prize and Lecture'' 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally resident in the United Kingdom on 1 January of the relevant year. Selection criteria include work in, influence on or service to mathematics, or recognition of lecturing gifts in the field of mathematics. Previous recipients of top LMS prizes or medals are ineligible for nomination. History The London Mathematical Society dates back to 1864. Augustus De Morgan's wife, writing after his death described how the London Mathematical Society was founded: It was in the year 1864 that Mr Arthur Cowper Ranyard and George De Morgan (Augustus De Morgan's son) were discussing mathematical problems during a walk in the streets, when it struck them that it would be very nice to have a society to which discoveries in mathematics could be brought, and wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stallings–Zeeman Theorem
In mathematics, the Stallings–Zeeman theorem is a result in algebraic topology, used in the proof of the Poincaré conjecture for dimension greater than or equal to five. It is named after the mathematicians John R. Stallings and Christopher Zeeman. Statement of the theorem Let ''M'' be a finite simplicial complex of dimension dim(''M'') = ''m'' ≥ 5. Suppose that ''M'' has the homotopy type of the ''m''-dimensional sphere S''m'' and that ''M'' is locally piecewise linearly homeomorphic to ''m''-dimensional Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ... R''m''. Then ''M'' is homeomorphic to S''m'' under a map that is piecewise linear except possibly at a single point ''x''. That is, ''M'' \ is piecewise linearly homeomorphic to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
