Criteria for components of a function space to be homotopy equivalent

• Autores: Gregory Lupton, Samuel Bruce Smith
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 1, 2008, págs. 95-106
• Idioma: inglés
• DOI: 10.1017/s0305004108001175
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• Resumen

  • 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.