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Existence theorems for H-space inverses

Published online by Cambridge University Press:  24 October 2008

Robin Sibson
Robin Sibson
Affiliation:
King's College, Cambridge, England
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Extract

We define an unbased H-space to be a pair (A, m) where A is a space and

is a map such that the maps La: x → m(a, x), Ra: x → m(x, a) are homotopy equivalences for all a ∈ A. This is the same as James's definition of an H'-space in (3); we follow his notation as far as possible. (A, m) is homotopy-associative if the maps m(m × 1) and m(l × m) are homotopic. A left (right) a-inverse (a ∈ A) is a map w: A → A such that the composition m(w × 1) d (w(1 × w) d) is homotopic to ka, the constant map to a. d denotes the diagonal map a → (a, a).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 19 - 21
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

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