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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the same $ N$-type conjecture for the suspension of the infinite complex projective space


Author: Dae-Woong Lee
Journal: Proc. Amer. Math. Soc. 137 (2009), 1161-1168
MSC (2000): Primary 55P15; Secondary 55S37, 55P40
Published electronically: October 20, 2008
MathSciNet review: 2457459
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09666-4
PII: S 0002-9939(08)09666-4
Keywords: Same $n$-type, Aut, commutator, Samelson (Whitehead) product
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.