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On the Gauss-Manin connection in cyclic homology


Getzler constructed a flat connection in the periodic cyclic homology, called the Gauss-Manin connection. In this paper we define this connection, and its monodromy, at the level of the periodic cyclic complex. The construction does not depend on an associator, and provides an explicit structure of a DG module over an auxiliary DG algebra. This paper is, to a large extent, an effort to clarify and streamline our work [4] with Yu.L. Daletsky.

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TitleOn the Gauss-Manin connection in cyclic homology
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 83-94
MathSciNet   MR2308582
CopyrightThe Author(s) 2007 (CC BY-SA)

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Boris Tsygan
Department of Mathematics, Northwestern University, Evanston, Illinois, USA Boris Tsygan Northwestern University 

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Boris Tsygan, On the Gauss-Manin connection in cyclic homology, Methods Funct. Anal. Topology 13 (2007), no. 1, 83-94.


@article {MFAT401,
    AUTHOR = {Tsygan, Boris},
     TITLE = {On the Gauss-Manin connection in cyclic homology},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {83-94},
      ISSN = {1029-3531},
  MRNUMBER = {MR2308582},
       URL = {},

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