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Dynamics of Cayley Forms
Kirill Krasnov
The most natural first-order PDEs to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. In this work, we investigate the natural second-order con…
math.DG2026
Variations on a theme of MacDowell-Mansouri
P. D. Alvarez, K. Krasnov
Inspired by the MacDowell-Mansouri formulation of four-dimensional General Relativity, we study a class of four-dimensional gauge-theoretic functionals obtained from the Pontryagin…
math.DG2025
Plebanski complex
Kirill Krasnov, Adam Shaw
As is very well-known, linearisation of the instanton equations on a 4-manifold gives rise to an elliptic complex of differential operators, the truncated (twisted) Hodge complex $…