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Criteria for components of a function space to be homotopy equivalent

Published online by Cambridge University Press:  01 July 2008

GREGORY LUPTON  and
SAMUEL BRUCE SMITH
GREGORY LUPTON
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland OH 44115, U.S.A. e-mail: [email protected]
SAMUEL BRUCE SMITH
Affiliation:
Department of Mathematics, Saint Joseph's University, Philadelphia, PA 19131, U.S.A. e-mail: [email protected]
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Abstract

We give a general method that may be effectively applied to the question of whether two components of a function space map(X, Y) have the same homotopy type. We describe certain group-like actions on map(X, Y). Our basic results assert that if maps f, g: X → Y are in the same orbit under such an action, then the components of map(X, Y) that contain f and g have the same homotopy type.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 95 - 106
Copyright
Copyright © Cambridge Philosophical Society 2008

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