Oct 18, 2024 · Idea 0.1 Integral cohomology or “ ordinary cohomology ” (see there) is the ordinary version of Whitehead-generalized cohomology, the one that is represented by the Eilenberg …

The rational homology of unordered configuration spaces of points on any surface was studied by Drummond-Cole and Knudsen. We compute the rational cohomology of configura-tion spaces …

The most famous of these spaces is B(R2, n): Fadell and Neuwirth showed that this space is an Eilenberg-Mac Lane space K(π, 1), with fundamental group isomorphic to Artin’s braid group …

Summary For any topological space X, let on space of n distinct points in X. The symmetric group Sn acts on Fn(X) by p Cn(X) = Fn(X)/Sn is the unordered configuration space. This thesis …

The The cohomology cohomology algebras algebras ofof ordered ordered configuration configuration spaces spaces ofof spheres spheres with with integral integral coefficients …

We could do a littple better by taking Xs+1 to be a ZG-module generating set of ker ds. From algebraic topology: Let X be a connected simplicial complex X with fundamental group G so …

Given an N‐dimensional compact closed oriented manifold M and a field lk, F. Cohen and L. Taylor have constructed a spectral sequence, ε(M, n, k), converging to the cohomology of the …

May 26, 2023 · Let Ck(R2) C k (R 2) be a k-points unordered configuration space of euclidean plane. It is a well known result of Arnold that the integral cohomology groups of degree bigger …

May 11, 2023 · We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with …

We compute the integral homology and cohomology groups of configuration spaces of two distinct points on a given real projective space. The explicit answer is related to the (known …