Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers.
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology, where one studies algebraic invariants of spaces, such as the fundamental weak ∞-groupoid.
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.
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.
Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory.
The mathematician Shmuel Aaron Weinberger is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was, from 1994 to 1996, the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, and he is currently the Andrew MacLeish Professor of Mathematics and chair of the Mathematics department at the University of Chicago.
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.
Ronald Brown FLSW 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.
Gunnar E. Carlsson is an American mathematician, working in algebraic topology. He is known for his work on the Segal conjecture, and for his work on applied algebraic topology, especially topological data analysis. He is a Professor Emeritus in the Department of Mathematics at Stanford University. He is the founder and president of the predictive technology company Ayasdi.
James Dillon Stasheff is an American mathematician, a professor emeritus of mathematics at the University of North Carolina at Chapel Hill. He works in algebraic topology and algebra as well as their applications to physics.
Jonathan Micah Rosenberg is an American mathematician, working in algebraic topology, operator algebras, K-theory and representation theory, with applications to string theory in physics.
Eric Mark Friedlander is an American mathematician who is working in algebraic topology, algebraic geometry, algebraic K-theory and representation theory.
Arthur Everett Pitcher was an American mathematician, known for early pioneering work on exact sequences and applying Morse theory to homotopy theory.
Ralph Louis Cohen is an American mathematician, specializing in algebraic topology and differential topology.
Aldridge Knight Bousfield, known as "Pete", was an American mathematician working in algebraic topology, known for the concept of Bousfield localization.
Dan Burghelea is a Romanian-American mathematician, academic, and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.
Alexander A. Voronov is a Russian-American mathematician specializing in mathematical physics, algebraic topology, and algebraic geometry. He is currently a Professor of Mathematics at the University of Minnesota and a Visiting Senior Scientist at the Kavli Institute for the Physics and Mathematics of the Universe.
