Tondo G. Higher Haantjes brackets and integrability (abstract)

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Speaker: Giorgio Tondo

Title: Higher Haantjes brackets and integrability

We propose a new, infinite class of brackets generalizing the Frölicher-Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not re-quire any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.

Slides: TondoAMVconf2021slides.pdf

Piergiulio Tempesta and Giorgio Tondo, Higher Haantjes Brackets and Integrability, Commun. Math. Phys. (2021),, arXiv:1809.05908

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.