On the Gauss-Manin connection in cyclic homology

Abstract

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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Article Information

Title	On the Gauss-Manin connection in cyclic homology
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 83-94
MathSciNet	MR2308582
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

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

Citation Example

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

BibTex

@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 = {http://mfat.imath.kiev.ua/article/?id=401},
}