Mathematical Proceedings of The Cambridge Philosophical Society
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.
Lupton, Gregory and Smith, Samuel Bruce, "Criteria for Components of A Function Space to Be Homotopy Equivalent" (2008). Mathematics Faculty Publications. 177.
© Cambridge Philosophical Society 2008. https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/criteria-for-components-of-a-function-space-to-be-homotopy-equivalent/02F180B7934357669853BB2FD93C5803