We introduce various classes of local maps: gradient, gradient-like, proper etc. We prove Parusiński's theorem for otopy classes of gradient local maps.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-6, author = {Piotr Bart\l omiejczyk and Piotr Nowak-Przygodzki}, title = {Gradient otopies of gradient local maps}, journal = {Fundamenta Mathematicae}, volume = {215}, year = {2011}, pages = {89-100}, zbl = {1229.55003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-6} }
Piotr Bartłomiejczyk; Piotr Nowak-Przygodzki. Gradient otopies of gradient local maps. Fundamenta Mathematicae, Tome 215 (2011) pp. 89-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-6/