Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary

Given an action of a discrete group G on a smooth compact manifold M with a boundary, we consider a class of operators generated by pseudodifferential operators on M and shift operators associated with the group action. For elliptic operators in this class, we obtain a classification up to stable homotopies and show that the group of stable homotopy classes of such problems is isomorphic to the K-group of the crossed product of the algebra of continuous functions on the cotangent bundle over the interior of the manifold and the group G acting on this algebra by automorphisms. © Savin A. Yu., Sternin B. Yu. 2016.

Authors
Savin A.Y. 1, 2 , Sternin B.Y. 1, 2
Publisher
Institute of Mathematics with Computing Centre
Number of issue
3
Language
English
Pages
122-129
Status
Published
Volume
8
Year
2016
Organizations
  • 1 RUDN University, Moscow Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 2 Leibniz Universität Hannover, Welfengarten 1, Hannover, D-30167, Germany
Keywords
Crossed product; Elliptic operator; G-operator; Homotopy classificationK-theory
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4167/