Iterated cyclic homology

Kodai Mathematical Journal

Masaaki Yokotani²  Katsuhiko Kuribayashi¹ 

[1] Department of Mathematical Sciences Faculty of Science, Shinshu University;Division of General Education Tsuyama National College of Technology

关键词: Borel cohomology;    Function spaces;    Iterated cyclic homology;    Sullivan minimal model;   

DOI  :  10.2996/kmj/1175287619

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(13)From the viewpoint of rational homotopy theory, we introduce an iterated cyclic homology of connected commutative differential graded algebras over the rational number field, which is regarded as a generalization of the ordinary cyclic homology. Let T be the circle group and $¥mathcal{F}$ (Tl, X) denote the function space of continuous maps from the l-dimensional torus Tl to an l-connected space X. It is also shown that the iterated cyclic homology of the differential graded algebra of polynomial forms on X is isomorphic to the rational cohomology algebra of the Borel space ET × T $¥mathcal{F}$ (Tl, X), where the T-action on $¥mathcal{F}$ (Tl, X) is induced by the diagonal action of T on the source space Tl.

【 授权许可】

Unknown