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The Homotopy of Simplicial Algebras

Published online by Cambridge University Press:  20 November 2018

Harry Lakser
Harry Lakser*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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In [6] Walter Taylor investigated the relationship between the algebraic structure of a topological algebra A and the group structure of its fundamental group π1(A) and of the higher homotopy groups πn(A),n > 1. The main result is that a variety satisfies a group law λ in homotopy (that is, π1) if and only if every group in the idempotent reduct of obeys λ. (The relevant definitions are in [6] and also § 2 of this paper.) A similar result is stated for the higher homotopy groups. As Taylor points out in the introduction, the hard part of the theorem is constructing a topological algebra in whose fundamental group may fail to obey λ; indeed, in [6] this is only done in detail for the commutative law, and the proof is rather computational.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 6 , 01 December 1980 , pp. 1411 - 1422
Copyright
Copyright © Canadian Mathematical Society 1980

References

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