Spaces which Look Like Quaternionic Projective n-Space
Copyright policy )Spaces which Look Like Quaternionic Projective n-Space
The projective n n -spaces which correspond to the various multiplicative structures on the three sphere are studied. Necessary and sufficient conditions for a projective n n -space to extend to a projective n + 1 n+1 -space are described. At each odd prime, an infinite family of exotic projective spaces is constructed. These exotic spaces are not homotopy equivalent, at the prime in question, to the classical quaternionic projective n n -space. It is also shown that these exotic projective n n -spaces do not occur as the finite skeleton of a classifying space for a group with the homotopy type of the three sphere.
infinite quaternionic projective space, An-structures, space whose loop space has the homotopy type of the 3-sphere, Homotopy equivalences in algebraic topology, Classifying spaces of groups and \(H\)-spaces in algebraic topology, Whitehead product, classifying space, Loop spaces
infinite quaternionic projective space, An-structures, space whose loop space has the homotopy type of the 3-sphere, Homotopy equivalences in algebraic topology, Classifying spaces of groups and \(H\)-spaces in algebraic topology, Whitehead product, classifying space, Loop spaces
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