A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-5, author = {Andrzej Czarnecki}, title = {Cutting description of trivial 1-cohomology}, journal = {Annales Polonici Mathematici}, volume = {111}, year = {2014}, pages = {181-184}, zbl = {1308.54018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-5} }
Andrzej Czarnecki. Cutting description of trivial 1-cohomology. Annales Polonici Mathematici, Tome 111 (2014) pp. 181-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-5/