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PreprintarXiv licencearXiv

A closed formula for the Poisson cohomology of scalar Dubrovin-Novikov brackets in arbitrary dimension

  • Matteo Casati
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Abstract

The structure of the Poisson cohomology groups for scalar Poisson brackets of Dubrovin-Novikov type with D independent variables has been first described in arXiv:1512.05744 ; in that work, a complete dimensional counting was provided for D=2, and some numerical results exhibited for D=3, D=4. Here, we prove a formula for the dimensional counting of the Poisson cohomology for arbitrary D. Moreover, we show how to obtain canonical representatives for each cohomology class.

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Cite

BibTeXRIS
BibTeX
@misc{casati2026closed,
  title = {{A closed formula for the Poisson cohomology of scalar Dubrovin-Novikov brackets in arbitrary dimension}},
  author = {Matteo Casati},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00531},
  eprint = {2611.00531},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00531},
}
RIS
TY  - UNPB
TI  - A closed formula for the Poisson cohomology of scalar Dubrovin-Novikov brackets in arbitrary dimension
AU  - Matteo Casati
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00531
UR  - https://arxiv.org/abs/2611.00531
AB  - The structure of the Poisson cohomology groups for scalar Poisson brackets of Dubrovin-Novikov type with D independent variables has been first described in arXiv:1512.05744 ; in that work, a complete dimensional counting was provided for D=2, and some numerical results exhibited for D=3, D=4. Here, we prove a formula for the dimensional counting of the Poisson cohomology for arbitrary D. Moreover, we show how to obtain canonical representatives for each cohomology class.
ER  -