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This article is cited in 1 scientific paper (total in 1 paper)
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.
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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:
   
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. J., 8:3 (2016), 122–129
Citation in format AMSBIB
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This publication is cited in the following articles:
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A. Yu. Savin, “O gomotopicheskoi klassifikatsii ellipticheskikh zadach so szhatiyami i $K$-gruppakh sootvetstvuyuschikh $C^*$-algebr”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 164–179
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