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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]
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} .
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
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, 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 .
In mathematics, specifically algebraic topology, the mapping cylinder [1] of a continuous function between topological spaces and is the quotient = (([,])) / where the denotes the disjoint union, and ~ is the equivalence relation generated by
Let X be a topological space and A, B be two subspaces whose interiors cover X. (The interiors of A and B need not be disjoint.) The Mayer–Vietoris sequence in singular homology for the triad (X, A, B) is a long exact sequence relating the singular homology groups (with coefficient group the integers Z) of the spaces X, A, B, and the intersection A∩B. [8]
In algebraic geometry and algebraic topology, branches of mathematics, A 1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to Fabien Morel and Vladimir Voevodsky.