 Hochschild, Cyclic and Periodic Cyclic HomologyNeculai S. Teleman
Chapter Chapter 3 in From Differential Geometry to Non-commutative Geometry and Topology, 2019, pp 169-231 from Springer Abstract: Abstract Hochschild homology (along with cyclic and periodic cyclic homologies) plays in the non-commutative geometry the role which de Rham cohomology plays in the classical geometry. It is defined for any associative algebra. The Hochschild chains over the algebra A $$\mathcal {A}$$ are not localised and the operations with the chains over the algebra A $$\mathcal {A}$$ are not commutative. If the algebra were the algebra of differentiable functions over a topological manifold M, the corresponding Hochschild chains would be differentiable functions over M N. Cyclic/periodic cyclic homology of the A $$\mathcal {A}$$ were introduced to extend the Chern–Weil characteristic classes to idempotents over A $$\mathcal {A}$$ . Cyclic/periodic cyclic homology represents the minimal algebraic structure for which the Chern–Weil construction works. The cyclic/periodic cyclic homology of the algebra of differentiable functions constitutes the link between the classical differential geometry and non-commutative geometry. Date: 2019 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28433-6_3 Ordering information: This item can be ordered from DOI: 10.1007/978-3-030-28433-6_3 Access Statistics for this chapter More chapters in Springer Books from Springer |
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