In this paper we study notions of homotopy in the Newtonian space of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions we prove a compactness result for sequences in homotopy classes with controlled homotopies.
Cite this article
Elefterios Soultanis, Homotopy classes of Newtonian maps. Rev. Mat. Iberoam. 33 (2017), no. 3, pp. 951–994DOI 10.4171/RMI/960