On the center of the rational cohomology algebra of some loop spaces with respect to the Pontryagin product.
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.
scientific article; zbMATH DE number 5759015