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Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology
Balodi, Mamta1 ; Banerjee, Abhishek1
1 Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 617-652

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We replace a ring with a small ℂ-linear category 𝒞, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of 𝒞. We show that this categorified Chern character is homotopy invariant and is well-behaved with respect to the periodicity operator in cyclic cohomology. For this, we also obtain a description of cocycles and coboundaries in the cyclic cohomology of 𝒞 (and more generally, in the Hopf cyclic cohomology of a Hopf-module category) by means of DG-semicategories equipped with a trace on endomorphism spaces.

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DOI : 10.5802/crmath.429
Classification : 18E05, 47A53, 53C99, 58B34

Balodi, Mamta 1 ; Banerjee, Abhishek 1

1 Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Fredholm modules over categories, {Connes} periodicity and classes in cyclic cohomology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {617--652},
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Balodi, Mamta; Banerjee, Abhishek. Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology. Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 617-652. doi: 10.5802/crmath.429

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