On the same $N$-type conjecture for the suspension of the infinite complex projective space
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Abstract:
Let $[\varphi _{i_{k}},[\varphi _{i_{k-1}},\cdots ,[\varphi _{i_{1}}, \varphi _{i_{2}}],\cdots ]]$ be an iterated commutator of self-maps $\varphi _{i_{j}}$ on the suspension of the infinite complex projective space. In this paper, we produce useful self-maps of the form $I + [\varphi _{i_{k}},[\varphi _{i_{k-1}},\cdots , [\varphi _{i_{1}}, \varphi _{i_{2}}],\cdots ]]$, where $+$ means the addition of maps on the suspension structure of $\Sigma {\mathbb {C}}P^{\infty }$. We then give the answer to the conjecture saying that the set of all the same homotopy $n$-types of the suspension of the infinite complex projective space is the one element set consisting of a single homotopy type.References
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Additional Information
- Dae-Woong Lee
- Affiliation: Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju, Jeonbuk 561-756, Republic of Korea
- Email: dwlee@math.chonbuk.ac.kr
- Received by editor(s): February 28, 2008
- Received by editor(s) in revised form: April 28, 2008
- Published electronically: October 20, 2008
- Additional Notes: This paper was (partially) supported by the Chonbuk National University funds for overseas research, 2008
- Communicated by: Paul Goerss
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1161-1168
- MSC (2000): Primary 55P15; Secondary 55S37, 55P40
- DOI: https://doi.org/10.1090/S0002-9939-08-09666-4
- MathSciNet review: 2457459