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The homotopy decomposition of the suspension of a non-simply-connected five-manifold
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 17 April 2024, pp. 1-29
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- Article
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In this paper we determine the homotopy types of the reduced suspension space of certain connected orientable closed smooth $five$
-manifolds. As applications, we compute the reduced $K$
-groups of $M$
and show that the suspension map between the third cohomotopy set $\pi ^3(M)$
and the fourth cohomotopy set $\pi ^4(\Sigma M)$
is a bijection.
