منابع مشابه
Power Operations and Coactions in Highly Commutative Homology Theories
Power operations in the homology of infinite loop spaces, and H∞ or E∞ ring spectra have a long history in algebraic topology. In the case of ordinary mod p homology for a prime p, the power operations of Kudo, Araki, Dyer and Lashof interact with Steenrod operations via the Nishida relations, but for many purposes this leads to complicated calculations once iterated applications of these funct...
متن کاملHomology Operations in Symmetric Homology
Symmetric homology of a unital algebra A over a commutative ground ring k has been defined using derived functors and the symmetric bar construction of Fiedorowicz, in an analogous way as cyclic, dihedral or quaternionic homology has been defined. In this paper, it is found that the HS∗(A) admits Dyer-Lashoff homology operations, and indeed, there is a Pontryagin product structure making HS∗(A)...
متن کاملBrowder operations and heat kernel homology
We define a stochastic homology theory for the n-fold based loop space of a compact manifold related to the heat kernel diffeology and we define over it Browder operations.
متن کاملHomology and Derived Series of Groups
In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a solvable completion of a group that is analogous to the Malcev completion, with the role of the lower central series replaced by the...
متن کاملHomology and Derived P-series of Groups
We prove that groups that are Zp-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings’ 1963 result for the p−lower-central series. In fact we prove a stronger theorem that is analogous to Dwyer’s extensions of Stallings’ results. Similarly, spaces that are Zp-homology equivalent have isomorphic fundamental groups modulo any term of their ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1983
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500005231