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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1971-0279763-0
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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DOI: https://doi.org/10.1090/S0002-9947-1971-0279763-0
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

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