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arXiv · 1805.02876

The same $n$-type structure of the suspension of the wedge products of the Eilenberg-MacLane spaces

Dae-Woong Lee
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Abstract

For a connected CW-complex, we let $SNT(X)$ be the set of all homotopy types $[Y]$ such that the Postnikov approximations $X^{(n)}$ and $Y^{(n)}$ of $X$ and $Y$, respectively, are homotopy equivalent for all positive integers $n$. In 1992, McGibbon and M{\o}ller (\cite[page 287]{MM}) raised the following question: Is $SNT(\Sigma \mathbb C P^\infty) = *$ or not? In this article, we give an answer to the more generalized version of this query: The set of all the same $n$-types of the suspended wedge sum of the Eilenberg-MacLane spaces of various types of both even and odd integers is the set which consists of only one element as a single homotopy type of itself.

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Dae-Woong Lee. 2018-05-08. The same $n$-type structure of the suspension of the wedge products of the Eilenberg-MacLane spaces. https://arxiv.org/abs/1805.02876

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