منابع مشابه
Higher homotopy operations and the cohomology of diagrams
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 ...
متن کاملHigher 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...
متن کاملHigher Homotopy Commutativity of H-spaces with Finitely Generated Cohomology
Suppose X is a simply connected mod p H-space such that the mod p cohomology H∗(X;Z/p) is finitely generated as an algebra. Our first result shows that if X is an An-space, then X is the total space of a principal An-fibration with base a finite An-space and fiber a finite product of CP∞s. As an application of the first result, it is shown that if X is a quasi Cp-space, then X is homotopy equiv...
متن کامل4 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...
متن کاملLoop Spaces and Homotopy Operations
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of K-Theory
سال: 2010
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is010001011jkt099