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| On the Same $n$-Types for the Wedges of the Eilenberg-Maclane Spaces |
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Citation： |
Dae-Woong LEE.On the Same $n$-Types for the Wedges of the Eilenberg-Maclane Spaces[J].Chinese Annals of Mathematics B,2016,37(6):951~962 |
| Page view： 1571
Net amount： 1232 |
Authors： |
Dae-Woong LEE; |
Foundation： |
This work was supported by the Basic Science Research
Program through the National Research Foundation of Korea (NRF, in
short) funded by the Ministry of Education
(No.NRF-2015R1D1A1A09057449). |
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| Abstract： |
Given a connected CW-space $X,\ SNT(X)$ denotes the set of all
homotopy types $[X']$ such that the Postnikov approximations
$X^{(n)}$ and $X'^{(n)}$ are homotopy equivalent for all $n$. The
main purpose of this paper is to show that the set of all the same
homotopy $n$-types of the suspension of the wedges of the
Eilenberg-MacLane spaces is the one element set consisting of a
single homotopy type of itself, i.e., $SNT(\Sigma (K(\Bbb Z, 2a_1)
\vee K(\Bbb Z, 2a_2) \vee \cdots \vee K(\Bbb Z, 2a_k))) = *$ for
$a_1 < a_2 < \cdots < a_k$, as a far more general conjecture than
the original one of the same $n$-type posed by McGibbon and
M{\o}ller (in [McGibbon, C. A. and M{\o}ller, J. M., On infinite
dimensional spaces that are rationally equivalent to a bouquet of
spheres, Proceedings of the 1990 Barcelona Conference on Algebraic
Topology, Lecture Notes in Math., {\bf 1509}, 1992, 285--293].) |
Keywords： |
Same $n$-type, Aut, Basic Whitehead product, Samelson product, Bott-Samelson theorem, Tensor algebra, Cartan-Serre theorem, Hopf-Thom theorem |
Classification： |
55P15, 55S37, 55P62 |
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