Properties of Anick's spaces

Author:
Stephen D. Theriault

Journal:
Trans. Amer. Math. Soc. **353** (2001), 1009-1037

MSC (2000):
Primary 55P45; Secondary 55Q15

Published electronically:
August 8, 2000

MathSciNet review:
1709780

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Abstract: We prove three useful properties of Anick's space . First, at odd primes a map from into a homotopy commutative, homotopy associative -space can be extended to a unique -map from into . Second, at primes larger than , is itself homotopy commutative and homotopy associative. And third, the first two properties combine to show that the order of the identity map on is .

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Additional Information

**Stephen D. Theriault**

Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60607

Address at time of publication:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903

Email:
st7b@virginia.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02623-4

Keywords:
$H$-spaces,
universal Whitehead product,
exponent

Received by editor(s):
December 4, 1998

Published electronically:
August 8, 2000

Additional Notes:
The author was supported in part by an NSERC Postdoctoral Fellowship.

Article copyright:
© Copyright 2000
American Mathematical Society