Resumen de Criteria for components of a function space to be homotopy equivalent

Gregory Lupton, Samuel Bruce Smith

• 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.