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.
In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate.
Luitzen Egbertus Jan Brouwer, usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the 20th century, he is known as the founder of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension.
Raoul Bott was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
Anatoly Timofeevich Fomenko is a Soviet and Russian conspiracy theorist, mathematician, professor at Moscow State University, well-known as a topologist, and a member of the Russian Academy of Sciences. He is the author of a fictitious pseudoscientific history known as New Chronology, based on works of Russian-Soviet writer Nikolai Alexandrovich Morozov. He is also a member of the Russian Academy of Natural Sciences (1991).
Counterexamples in Topology is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr.
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
In mathematics, a structure is a set endowed with some additional features on the set. Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance.
Geometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical Sciences Publishers, a nonprofit academic publishing organisation.
Mary Ellen Rudin was an American mathematician known for her work in set-theoretic topology. In 2013, Elsevier established the Mary Ellen Rudin Young Researcher Award, which is awarded annually to a young researcher, mainly in fields adjacent to general topology.
Topology was a peer-reviewed mathematical journal covering topology and geometry. It was established in 1962 and was published by Elsevier. The last issue of Topology appeared in 2009.
Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages.
William Browder is an American mathematician, specializing in algebraic topology, differential topology and differential geometry. Browder was one of the pioneers with Sergei Novikov, Dennis Sullivan and C. T. C. Wall of the surgery theory method for classifying high-dimensional manifolds. He served as president of the American Mathematical Society until 1990.
Mathematical Sciences Publishers is a nonprofit publishing company run by and for mathematicians. It publishes several journals and the book series Geometry & Topology Monographs. It is run from a central office in the Department of Mathematics at the University of California, Berkeley.
Experimental Mathematics is a quarterly scientific journal of mathematics published by A K Peters, Ltd. until 2010, now by Taylor & Francis. The journal publishes papers in experimental mathematics, broadly construed. The journal's mission statement describes its scope as follows: "Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses." As of 2013 the editor-in-chief is Sergei Tabachnikov.
The Journal of Differential Geometry is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book form called Surveys in Differential Geometry. It covers differential geometry and related subjects such as differential equations, mathematical physics, algebraic geometry, and geometric topology. The editor-in-chief is Shing-Tung Yau of Harvard University.
Ronald Brown is an English mathematician. Emeritus Professor in the School of Computer Science at Bangor University, he has authored many books and more than 160 journal articles.
Topology and Its Applications is a peer-reviewed mathematics journal publishing research on topology. It was established in 1971 as General Topology and Its Applications, and renamed to its current title in 1980. The journal currently publishes 18 issues each year in one volume. It is indexed by Scopus, Mathematical Reviews, and Zentralblatt MATH. Its 2004–2008 MCQ was 0.38 and its 2020 impact factor was 0.617.
Colin Rourke is a British mathematician who worked in PL topology, low-dimensional topology, differential topology, group theory, relativity and cosmology. He is an emeritus professor at the Mathematics Institute of the University of Warwick and a founding editor of the journals Geometry & Topology and Algebraic & Geometric Topology, published by Mathematical Sciences Publishers, where he is the vice chair of its board of directors.
