منابع مشابه
4 Homotopy Operations and Rational Homotopy Type
In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in...
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We provide a general definition of higher homotopy operations, encompassing most known cases, including higher Massey and Whitehead products, and long Toda brackets. These operations are defined in terms of the W -construction of Boardman and Vogt, applied to the appropriate diagram category; we also show how some classical families of polyhedra (including simplices, cubes, associahedra, and pe...
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We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking value in π∗X. These depend on first algebraically “delooping” the Π-algebra π∗X, using the H-space structure on X, and then trying to realize the delooped Π-algebra.
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In any 2-category C with zeros (for example the topological 2-category T op∗ of based spaces, based maps and track classes of homotopies) box bracket operations have been defined and studied by Hardie-Marcum-Oda [4]. These are secondary homotopy operations and if (as we will suppose) C admits a suspension functor Σ (see [3]) they take values in morphism groups HC(ΣW,X), here denoted π(ΣW,X), of...
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The modern understanding of the homotopy theory of spaces and spectra is organized by the chromatic philosophy, which relates phenomena in homotopy theory with the moduli of one-dimensional formal groups. In this paper, we describe how certain phenomena in K(n)-local homotopy can be computed from knowledge of isogenies of deformations of formal groups of height n. Mathematics Subject Classifica...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1971
ISSN: 0040-8735
DOI: 10.2748/tmj/1178242593