Jeffrey H. Smith | |
---|---|
Nationality | American |
Alma mater | Massachusetts Institute of Technology |
Scientific career | |
Fields | Mathematics |
Institutions | Purdue University |
Doctoral advisor | Daniel Kan |
Jeffrey Henderson Smith is a former professor of mathematics at Purdue University in Lafayette, Indiana. He received his Ph.D. from the Massachusetts Institute of Technology in 1981, under the supervision of Daniel Kan, [1] and was promoted to full professor at Purdue in 1999. [2] His primary research interest is algebraic topology; his best-cited work [3] consists of two papers in the Annals of Mathematics on "nilpotence and stable homotopy".
John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize
Daniel Gray "Dan" Quillen was an American mathematician.
In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are easier to compute.
In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one.
In mathematics, and specifically in the field of homotopy theory, the Freudenthal suspension theorem is the fundamental result leading to the concept of stabilization of homotopy groups and ultimately to stable homotopy theory. It explains the behavior of simultaneously taking suspensions and increasing the index of the homotopy groups of the space in question. It was proved in 1937 by Hans Freudenthal.
In mathematics, stable homotopy theory is that part of homotopy theory concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space , the homotopy groups stabilize for sufficiently large. In particular, the homotopy groups of spheres stabilize for . For example,
In mathematics, the Toda bracket is an operation on homotopy classes of maps, in particular on homotopy groups of spheres, named after Hiroshi Toda, who defined them and used them to compute homotopy groups of spheres in.
In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime p. It is described in more detail in Ravenel and Mahowald (2001). It is related to the EHP long exact sequence of Whitehead (1953); the name "EHP" comes from the fact that George W. Whitehead named 3 of the maps of his sequence "E", "H", and "P".
In mathematics, Arakelov theory is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions.
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.
In geometric topology, the dogbone space, constructed by R. H. Bing (1957), is a quotient space of three-dimensional Euclidean space such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to . The name "dogbone space" refers to a fanciful resemblance between some of the diagrams of genus 2 surfaces in R. H. Bing's paper and a dog bone. Bing (1959) showed that the product of the dogbone space with is homeomorphic to .
Mark Edward Mahowald was an American mathematician known for work in algebraic topology.
Douglas Conner Ravenel is an American mathematician known for work in algebraic topology.
In algebraic topology, the nilpotence theorem gives a condition for an element of the coefficient ring of a ring spectrum to be nilpotent, in terms of complex cobordism. It was conjectured by Douglas Ravenel (1984) and proved by Ethan S. Devinatz, Michael J. Hopkins, and Jeffrey H. Smith (1988).
In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 1984. It was earlier circulated in preprint. The problems involved have largely been resolved, with all but the "telescope conjecture" being proved in later papers by others. The telescope conjecture is now generally believed not to be true, though there are some conflicting claims concerning it in the published literature, and is taken to be an open problem. Ravenel's conjectures exerted influence on the field through the founding of the approach of chromatic homotopy theory.
Goro Nishida was a Japanese mathematician. He was a leading member of the Japanese school of homotopy theory, following in the tradition of Hiroshi Toda.
Sze-Tsen Hu, also known as Steve Hu, was a Chinese-American mathematician, specializing in homotopy theory.
Edgar Henry Brown, Jr. is an American mathematician specializing in algebraic topology, and for many years a professor at Brandeis University.
Jean Estelle Hirsh Rubin was an American mathematician known for her research on the axiom of choice. She worked for many years as a professor of mathematics at Purdue University. Rubin wrote five books: three on the axiom of choice, and two more on more general topics in set theory and mathematical logic.
Charles Waldo Rezk is an American mathematician, specializing in algebraic topology, category theory, and spectral algebraic geometry.