Topological methods in abstract algebra. cohomology theory of groups

Eilenberg, Samuel

doi:10.1090/s0002-9904-1949-09161-9

Cited by 48 publications

(10 citation statements)

References 28 publications

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“…Now we recall how one obtains the Steenrod operations for our future use. We consider the standard small free resolution [5] of a = {1; ; 2 ; : : : ; p−1 } :…”

Section: Algebraic Steenrod Operationsmentioning

confidence: 99%

Steenrod operations in SHC-algebras

Ndombol

Thomas

2004

Journal of Pure and Applied Algebra

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In this paper we use May's algebraic approach to Steenrod operation in conjunction with Munkholm's notion of shc-algebra in order to introduce what we call a -shc-algebra. ( is a cyclic group of order a ÿxed prime p.) We prove that the homology and the Hochschild homology of a -shc-algebra have natural Steenrod operations. Our main topological example is the free loop space. We prove that the Jones' isomorphism preserves Steenrod operations.

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“…Now we recall how one obtains the Steenrod operations for our future use. We consider the standard small free resolution [5] of a = {1; ; 2 ; : : : ; p−1 } :…”

Section: Algebraic Steenrod Operationsmentioning

confidence: 99%

Steenrod operations in SHC-algebras

Ndombol

Thomas

2004

Journal of Pure and Applied Algebra

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“…In diesem Anhang ste]len wit die Definitionen und S~tze der Kohomologietheorie yon Gruppen zusammen, die wir in der vorliegenden Arbeit benStigen (siehe [6,7]). …”

Section: Anhang I Kohomologietheorie Yon Gruppenunclassified

Mehrdeutige Funktionen zu gegebenen Divisoren auf einem Produktraum

Königsberger¹

1964

Math. Ann.

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“…Actually the case n = 1 may be treated separately (using the universal covering space) within the framework of the theory of spaces and complexes with operators (see [1] for complete references). This paper makes full use of the results and terminology of the preceding paper by S. Eilenberg and J.…”

Section: Relations Between Homology and Homotopy Groups Of Spaces IImentioning

confidence: 99%

“…This is the usual coboundary formula in the cohomology theory of groups [1], This second homomorphism is obtained by assigning to each cochain f e CG(7n ,n, G) a cochain K*f * Cq(S (X), G) defined for each q-simplex T e Sn(X)…”

Section: The Complexes K(7r N)mentioning

confidence: 99%