Homotopy commutativity of -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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We show that a simply connected homotopy associative and homotopy commutative mod -space with finitely generated mod cohomology is homotopy equivalent to a finite product of , , the three-connected cover and the homotopy fiber of the map for . Our result also shows that a connected -space in the sense of Sugawara with finitely generated mod cohomology has the homotopy type of a finite product of , and for .

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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