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Elliptic theory on manifolds with corners. II: homotopy classification and $$K$$-homology. (English) Zbl 1205.58018
Burghelea, Dan (ed.) et al., $$C^*$$-algebras and elliptic theory II. Selected papers of the international conference, Bȩdlewo, Poland, January 2006. Basel: Birkhäuser (ISBN 978-3-7643-8603-0/hbk). Trends in Mathematics, 207-226 (2008).
Summary: We establish the stable homotopy classification of elliptic pseudodifferential operators on manifolds with corners and show that the set of elliptic operators modulo stable homotopy is isomorphic to the $$K$$-homology group of some stratified manifold. By way of application, generalizations of some recent results due to Monthubert and Nistor are given.
[For part I of this paper, see the authors, ibid., 183–206 (2008; Zbl 1205.58017).]
For the entire collection see [Zbl 1134.58002].

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J05 Elliptic equations on manifolds, general theory 19K33 Ext and $$K$$-homology 35S35 Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc.