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Haynes Robert Miller (born January 29, 1948, in Princeton, New Jersey) [1] is an American mathematician specializing in algebraic topology.. Miller completed his undergraduate study at Harvard University and earned his PhD in 1974 under the supervision of John Coleman Moore at Princeton University with thesis Some Algebraic Aspects of the Adams–Novikov Spectral Sequence. [2]
In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory.In concrete terms, for any integer n there is a topological space , and these spaces are equipped with certain maps between them, so that for any topological space X, one obtains an abelian group structure on the set of homotopy classes of continuous maps from X to .
Haynes Miller: Sullivan conjecture: classifying spaces: Miller proved the version on mapping BG to a finite complex. 1987: Grigory Margulis: Oppenheim conjecture: diophantine approximation: Margulis proved the conjecture with ergodic theory methods. 1989: Vladimir I. Chernousov: Weil's conjecture on Tamagawa numbers: algebraic groups
In mathematics, and especially topology and differential geometry, a pinched torus (or croissant surface) is a kind of two-dimensional surface. It gets its name from its resemblance to a torus that has been pinched at a single point. A pinched torus is an example of an orientable, compact 2-dimensional pseudomanifold. [1]
Miller's theorem generalizes to a version of Sullivan's conjecture in which the action on is allowed to be non-trivial. In, [ 3 ] Sullivan conjectured that η is a weak equivalence after a certain p-completion procedure due to A. Bousfield and D. Kan for the group G = Z / 2 {\displaystyle G=Z/2} .
In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space and those of the spaces and .
The Brouwer fixed point theorem was one of the early achievements of algebraic topology, and is the basis of more general fixed point theorems which are important in functional analysis. The case n = 3 first was proved by Piers Bohl in 1904 (published in Journal für die reine und angewandte Mathematik ). [ 14 ]
In geometric topology, cobordisms are intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories are fundamental extraordinary cohomology theories, and categories of cobordisms are the domains of topological quantum field ...