Higher homotopy operations
نویسندگان
چکیده
منابع مشابه
Higher Homotopy Operations
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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Algebraic topology tries to answer problems of homotopy theory by translating them into algebra, using invariants such as the homotopy or cohomology groups of a space. These invariants, even when endowed with extra algebraic structure such as Whitehead products or Steenrod operations, rarely reflect fully the original homotopical information, and the additional data needed for a full invariant ...
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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 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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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2003
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-003-0494-2