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Homotopy commutativity of $H$-spaces with finitely generated cohomology


Authors: Yusuke Kawamoto and James P. Lin
Journal: Trans. Amer. Math. Soc. 353 (2001), 4481-4496
MSC (2000): Primary 55P45, 55P15; Secondary 55P65
DOI: https://doi.org/10.1090/S0002-9947-01-02791-X
Published electronically: May 9, 2001
MathSciNet review: 1851180
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Abstract:

We show that a simply connected homotopy associative and homotopy commutative mod $3$ $H$-space with finitely generated mod $3$ cohomology is homotopy equivalent to a finite product of $K({\mathbb Z},2)$, $Sp(2)$, the three-connected cover $Sp(2)\langle 3\rangle$and the homotopy fiber $Sp(2)\langle 3;3^i\rangle$of the map $[3^i]:Sp(2)\to K({\mathbb Z},3)$ for $i\ge 1$. Our result also shows that a connected $C_p$-space in the sense of Sugawara with finitely generated mod $p$ cohomology has the homotopy type of a finite product of $K({\mathbb Z},1)$, $K({\mathbb Z},2)$ and $K({\mathbb Z}/p^i,1)$ for $i\ge 1$.


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Additional Information

Yusuke Kawamoto
Affiliation: Department of Mathematics, Faculty of Science, Hiroshima University, Higashi–Hiroshima 739–8526, Japan
Address at time of publication: Department of Mathematics, National Defense Academy, Yokosuka 239–8686, Japan
Email: yusuke@cc.nda.ac.jp

James P. Lin
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112
Email: jimlin@euclid.ucsd.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02791-X
Keywords: $H$-space, $C_n$-space, Dror Farjoun localization functor
Received by editor(s): February 12, 1999
Received by editor(s) in revised form: September 18, 2000
Published electronically: May 9, 2001
Additional Notes: Partially supported by JSPS Research Fellowships for Young Scientists
Article copyright: © Copyright 2001 American Mathematical Society

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