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Some small aspherical spaces

Published online by Cambridge University Press:  09 April 2009

Eldon Dyer  and
A. T. Vasquez
A. T. Vasquez
Affiliation:
The Graduate SchoolCity University of New York, 33 West 42 Street New York, 10036 U. S. A.
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Let Sn denote the sphere of all points in Euclidean space Rn + 1 at a distance of 1 from the origin and Dn + 1 the ball of all points in Rn + 1 at a distance not exceeding 1 from the origin The space X is said to be aspherical if for every n ≧ 2 and every continuous mapping: f: Sn → X, there exists a continuous mapping g: Dn + 1 → X with restriction to the subspace Sn equal to f. Thus, the only homotopy group of X which might be non-zero is the fundamental group τ1(X, *) ≅ G. If X is also a cell-complex, it is called a K(G, 1). If X and Y are K(G, l)'s, then they have the same homotopy type, and consequently

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 332 - 352
Copyright
Copyright © Australian Mathematical Society 1973

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