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John Hempel
John Paul Hempel ( Salt Lake City, Utah, October 14, 1935 ─ Rice Lake, Wisconsin, January 13, 2022) was an American mathematician specialising in geometric topology, in particular the topology of 3-manifolds and associated algebraic problems, mainly in group theory. Early life and career Hempel was born in Salt Lake City, Utah. In 1957 he graduated from the University of Utah with a degree in mathematics. In 1962, he defended his thesis at the University of Wisconsin-Madison, under the supervision of R. H. Bing. He was a professor at Rice University until the time of his death. He was married to Edith, whom he married on September 1, 1965, in Houston, Texas. He had 1 son and 3 grandchildren. Outside of mathematics, Hempel was a nature enthusiast. As a child he was adventurous, and taught himself to mountain bike. He was also fascinated by camping, climbing, skiing and boating. In addition, he knew how to play the piano. In 2013, Hempel was elected a fellow of the A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salt Lake City, Utah
Salt Lake City (often shortened to Salt Lake and abbreviated as SLC) is the Capital (political), capital and List of cities and towns in Utah, most populous city of Utah, United States. It is the county seat, seat of Salt Lake County, Utah, Salt Lake County, the most populous county in Utah. With a population of 200,133 in 2020, the city is the core of the Salt Lake City metropolitan area, which had a population of 1,257,936 at the 2020 census. Salt Lake City is further situated within a larger metropolis known as the Salt Lake City–Provo–Orem Combined Statistical Area, Salt Lake City–Ogden–Provo Combined Statistical Area, a corridor of contiguous urban and suburban development stretched along a segment of the Wasatch Front, comprising a population of 2,746,164 (as of 2021 estimates), making it the 22nd largest in the nation. It is also the central core of the larger of only two major urban areas located within the Great Basin (the other being Reno, Nevada). Salt Lake C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skiing
Skiing is the use of skis to glide on snow. Variations of purpose include basic transport, a recreational activity, or a competitive winter sport. Many types of competitive skiing events are recognized by the International Olympic Committee (IOC), and the International Ski Federation (FIS). History Skiing has a history of almost five millennia. Although modern skiing has evolved from beginnings in Scandinavia, it may have been practiced more than 100 centuries ago in what is now China, according to an interpretation of ancient paintings. However, this continues to be debated. The word "ski" comes from the Old Norse word "skíð" which means to "split piece of wood or firewood". Asymmetrical skis were used in northern Finland and Sweden until at least the late 19th century. On one foot, the skier wore a long straight non-arching ski for sliding, and a shorter ski was worn on the other foot for kicking. The underside of the short ski was either plain or covered with animal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rice University Faculty
Rice is the seed of the grass species ''Oryza sativa'' (Asian rice) or less commonly ''Oryza glaberrima'' (African rice). The name wild rice is usually used for species of the genera ''Zizania'' and ''Porteresia'', both wild and domesticated, although the term may also be used for primitive or uncultivated varieties of ''Oryza''. As a cereal grain, domesticated rice is the most widely consumed staple food for over half of the world's human population,Abstract, "Rice feeds more than half the world's population." especially in Asia and Africa. It is the agricultural commodity with the third-highest worldwide production, after sugarcane and maize. Since sizable portions of sugarcane and maize crops are used for purposes other than human consumption, rice is the most important food crop with regard to human nutrition and caloric intake, providing more than one-fifth of the calories consumed worldwide by humans. There are many varieties of rice and culinary preferences tend to vary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2022 Deaths
The following notable deaths occurred in 2022. Names are reported under the date of death, in alphabetical order. A typical entry reports information in the following sequence: * Name, age, country of citizenship at birth, subsequent nationality (if applicable), what subject was noted for, cause of death (if known), and reference. December 25 * Chalapathi Rao, 78, Indian actor and producer, heart attack. (death announced on this date) 24 *Vittorio Adorni, 85, Italian road racing cyclist. *Cotton Davidson, 91, American football player ( Baltimore Colts, Dallas Texans, Oakland Raiders). (death announced on this date) *Franco Frattini, 65, Italian politician and magistrate, twice minister of foreign affairs, twice of public administration, European commissioner for justice (2004–2008), cancer. *Madosini, 78, South African musician. *Barry Round, 72, Australian footballer (Sydney, Footscray, Williamstown), organ failure. *Royal Applause, 29, British Thoroughbred racehorse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1935 Births
Events January * January 7 – Italian premier Benito Mussolini and French Foreign Minister Pierre Laval conclude Franco-Italian Agreement of 1935, an agreement, in which each power agrees not to oppose the other's colonial claims. * January 12 – Amelia Earhart becomes the first person to successfully complete a solo flight from Hawaii to California, a distance of 2,408 miles. * January 13 – A plebiscite in the Saar (League of Nations), Territory of the Saar Basin shows that 90.3% of those voting wish to join Germany. * January 24 – The first canned beer is sold in Richmond, Virginia, United States, by Gottfried Krueger Brewing Company. February * February 6 – Parker Brothers begins selling the board game Monopoly (game), Monopoly in the United States. * February 13 – Richard Hauptmann is convicted and sentenced to death for the kidnapping and murder of Charles Lindbergh Jr. in the United States. * February 15 – The discovery and clinical development of ... [...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] |
Curve Complex
In mathematics, the curve complex is a simplicial complex ''C''(''S'') associated to a finite-type surface ''S'', which encodes the combinatorics of simple closed curves on ''S''. The curve complex turned out to be a fundamental tool in the study of the geometry of the Teichmüller space, of mapping class groups and of Kleinian groups. It was introduced by W.J.Harvey in 1978. Curve complexes Definition Let S be a finite type connected oriented surface. More specifically, let S=S_ be a connected oriented surface of genus g\ge 0 with b\ge 0 boundary components and n\ge 0 punctures. The ''curve complex'' C(S) is the simplicial complex defined as follows: *The vertices are the free homotopy classes of essential (neither homotopically trivial nor peripheral) simple closed curves on S; *If c_1, \ldots, c_n represent distinct vertices of C(S), they span a simplex if and only if they can be homotoped to be pairwise disjoint. Examples For surfaces of small complexity (essen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residually Finite Group
{{unsourced, date=September 2022 In the mathematical field of group theory, a group ''G'' is residually finite or finitely approximable if for every element ''g'' that is not the identity in ''G'' there is a homomorphism ''h'' from ''G'' to a finite group, such that :h(g) \neq 1.\, There are a number of equivalent definitions: *A group is residually finite if for each non-identity element in the group, there is a normal subgroup of finite index not containing that element. *A group is residually finite if and only if the intersection of all its subgroups of finite index is trivial. *A group is residually finite if and only if the intersection of all its normal subgroups of finite index is trivial. *A group is residually finite if and only if it can be embedded inside the direct product of a family of finite groups. Examples Examples of groups that are residually finite are finite groups, free groups, finitely generated nilpotent groups, polycyclic-by-finite groups, finite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-manifold
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solids; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world. In general In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Group
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger case of homeomorphic) have isomorphic fundamental groups. The fundamental group of a topological space X is denoted by \pi_1(X). Intuition Start with a space (for example, a surface), and some point in it, and all the loops both starting and ending at this point— paths that start at this point, wander around and eventually return to the starting point. Two loops can be combined in an obvious way: travel along the first loop, then along the second. Two loops are considered equivalent if one can be deformed into the other without breakin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
