A Künneth theorem for the cyclic homology of A-infinity algebras

Abstract

The cyclic homology of a ℤ/2ℤ-graded, smooth and proper A_∞ category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A_∞ algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A_∞ tensor product A⊗_∞ B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A⊗_∞ B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A_∞ algebras developed in \cite{amorim2016tensor}.

Symbols at infinity and Lie algebras of vector fields
Emile Bouaziz
arXiv22 Sep 2026PreprintCC BY 4.0Full textAlgebra & number theoryarXiv
The Hochschild (co)homology of gentle algebras
Cristian Chaparro, Sibylle Schroll, Andrea Solotar +1
Journal of Algebra4 Jun 2026Peer-reviewedLicence not statedFull text13 citedGeometry & topologyOpenAlex
Morse homology of nonsingular Morse-Smale foliations and its duality theorem
Shigeaki Miyoshi
arXiv3 Nov 2026PreprintarXiv licenceFull textGeometry & topologyarXiv
Quantitative K-homology of uniform Roe algebras
Hao Guo, Chenxi Wang, Guoliang Yu
arXiv27 Oct 2026PreprintarXiv licenceFull textAlgebra & number theory Analysis & PDEsarXiv
A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties
Jules Chenal
Annales Henri Lebesgue16 Oct 2026Peer-reviewedCC BY 4.0Full textAlgebra & number theory Geometry & topologyHAL

Cite

BibTeX RIS

BibTeX

@misc{azubuike2026künneth,
  title = {{A Künneth theorem for the cyclic homology of A-infinity algebras}},
  author = {Henry Azubuike},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30164},
  eprint = {2610.30164},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30164},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - A Künneth theorem for the cyclic homology of A-infinity algebras
AU  - Henry Azubuike
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.30164
UR  - https://arxiv.org/abs/2610.30164
AB  - The cyclic homology of a ℤ/2ℤ-graded, smooth and proper A_∞ category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A_∞ algebras A and B with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the A_∞ tensor product A⊗_∞ B and show that it respects the EP-structures. As an application, we show that if A and B are equipped with weak Calabi-Yau structures, then A⊗_∞ B also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on A and B compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of A_∞ algebras developed in \cite{amorim2016tensor}.
ER  -

Abstract

Related

Cite