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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 3, Pages 126–134 (Mi ufa330)  

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

A. Yu. Savinab, B. Yu. Sterninab

a Peoples Friendship University of Russia, Moscow
b Leibniz Universitat Hannover, Welfengarten 1, D-30167 Hannover, Germany

Abstract: 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.

Keywords: elliptic operator, homotopy classification, $K$-theory, crossed product, $G$-operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-08392
16-01-00373
Ministry of Education and Science of the Russian Federation 02.a03.21.0008
Немецкое научно-исследовательское общество


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English version:
Ufa Mathematical Journal, 2016, 8:3, 122–129 (PDF, 340 kB); https://doi.org/10.13108/2016-8-3-122

Bibliographic databases:

Document Type: Article
UDC: 515.168.5+517.986.32
MSC: Primary 58J32; Secondary 58J40, 46L80, 35S15
Received: 18.05.2016

Citation: A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary”, Ufimsk. Mat. Zh., 8:3 (2016), 126–134; Ufa Math. Journal, 8:3 (2016), 122–129

Citation in format AMSBIB
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