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Transactions of the American Mathematical Society

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The space of retractions of the $2$-sphere and the annulus

Author: Neal R. Wagner
Journal: Trans. Amer. Math. Soc. 158 (1971), 319-329
MSC: Primary 54.28
MathSciNet review: 0279763
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Abstract: Given a manifold $M$, there is an embedding $\Lambda$ of $M$ into the space of retractions of $M$, taking each point to the retraction of $M$ to that point. Considering $\Lambda$ as a map into the connected component containing its image, we prove that $\Lambda$ is a weak homotopy equivalence for two choices of $M$, namely, the $2$-sphere and the annulus.

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Keywords: Retract, retraction, two-manifold, two-sphere, annulus, homotopy equivalence, weak homotopy equivalence, function space, compact-open topology, selection
Article copyright: © Copyright 1971 American Mathematical Society