This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-11, author = {Bertrand Monthubert}, title = {Contribution of noncommutative geometry to index theory on singular manifolds}, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {221-237}, zbl = {1147.58021}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-11} }
Bertrand Monthubert. Contribution of noncommutative geometry to index theory on singular manifolds. Banach Center Publications, Tome 75 (2007) pp. 221-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-11/