Geodesic
Noncommutative geometry and analysis
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 61-81.

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One of the main problems of noncommutative geometry is the translation of fundamental notions of analysis, topology, and differential geometry onto the language of Banach algebras. In this paper, we present a number of results of this kind focusing the attention on the noncommutative interpretation of the notions of differential and integral. Our presentation is based on the monographs Noncommutative Geometry by A. Connes and Elements of Noncommutative Geometry by J. M. Gracia-Bondia, J. C. Varilly, and H. Figueroa.
Keywords: $C^*$-algebra, Dixmier trace, differential graded algebra, cycle, Fredholm module, Chern cocycle.
Mots-clés : Wodzicki residue 
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     author = {A. G. Sergeev},
     title = {Noncommutative geometry and analysis},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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A. G. Sergeev. Noncommutative geometry and analysis. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 61-81. http://geodesic.mathdoc.fr/item/INTO_2017_137_a3/