On the center of the rational cohomology algebra of some loop spaces with respect to the Pontryagin product.
type: Item
instance of: scholarly article
title: On the center of the rational cohomology algebra of some loop spaces with respect to the Pontryagin product.
zbMATH Open document ID: 1199.55004
DOI: 10.3103/S002713220802006X
author: A. Yu. Onishchenko
published in: Moscow University Mathematics Bulletin
publication date: 2010-07-21T00:00:00Z
review text: In this paper the author presents results of the computation of the center of the rational cohomology algebra \(H^*(\Omega X;\mathbb Q)\) of loop spaces of one-connected four-dimensional manifolds with Pontryagin product. In the known results by Milnor and Moore \(H^*(\Omega X)\) is presented in the form of a universal enveloping Lie algebra \(\pi_*(\Omega X)\) considered with the Whitehead--Samelson bracket. Neisendorfer obtained the representation of the algebra \(\pi_*(\Omega X)\otimes \mathbb Q\) via generators and relations in the case when \(X\) is a one-connected four-dimensional manifold. By means of this representation the center \(Z(H^*(\Omega X;\mathbb Q))\) is computed in this paper.
Mathematics Subject Classification ID: 55N45
Mathematics Subject Classification ID: 55N10
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 5759015
zbMATH Keywords: algebra representation
zbMATH Keywords: calculation of center
MaRDI profile type: Publication
cites work: A Connection Between the Whitehead and the Pontryagin Product
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description: scientific article; zbMATH DE number 5759015