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Then this algebra is a minimal Sullivan algebra that is not formal. The cohomology algebra has nontrivial components only in dimension 2, 3, 6, generated respectively by a, b, and . Any homomorphism from V to its cohomology algebra would map y to 0 and x to a multiple of b; so it would map to 0.
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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} .
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems.
Daniel Gray Quillen (June 22, 1940 – April 30, 2011) was an American mathematician.He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
A commonly cited example is the Dwork construction of the Picard–Fuchs equation.Let (,,) be the elliptic curve + + =.Here, is a free parameter describing the curve; it is an element of the complex projective line (the family of hypersurfaces in dimensions of degree n, defined analogously, has been intensively studied in recent years, in connection with the modularity theorem and its ...
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [4] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...
Dennis Parnell Sullivan (born February 12, 1941) 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 .
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