Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0279763
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54.28

Retrieve articles in all journals with MSC: 54.28

Additional Information

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