HOMOTOPICAL EXCISION , AND HUREWICZ THEOREMS , FOR n-CUBES OF SPACES ∗

@inproceedings{Brown1987HOMOTOPICALE,
title={HOMOTOPICAL EXCISION , AND HUREWICZ THEOREMS , FOR n-CUBES OF SPACES ∗},
author={Ronald Brown and Jean-Louis Loday},
year={1987}
}

where e is induced by the ‘excision’ inclusion. That e is an isomorphism in a range of dimensions is shown by the classical Blakers-Massey triad connectivity theorem: if A, B, and A∩B are connected, {A,B} is an open cover of X and (A, A ∩ B) is p-connected, (B, A ∩ B) is q-connected, then the triad (X; A,B) is (p + q)-connected. (See, for example, [11, p. 211].) Further, if p, q > 2 and π1(A∩B) = 0, the critical group πp+q+1(X; A, B) is described in [2] as a tensor product of abelian groups πp… CONTINUE READING