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arXiv · 2304.12103

Stability of fixed points of Dirac structures

Karandeep Jandu Singh·Marco Zambon
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Abstract

Given an $L_{\infty}$-algebra $V$ and an $L_{\infty}$-subalgebra $W$, we give sufficient conditions for all small Maurer-Cartan elements of $V$ to be equivalent to Maurer-Cartan elements lying in $W$. As an application, we obtain a stability criterion for fixed points of a Dirac structure (for instance a twisted Poisson structure), i.e. points where the corresponding leaf is zero-dimensional. The criterion guarantees that any nearby Dirac structure also has a fixed point.

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Karandeep Jandu Singh, Marco Zambon. 2023-04-24. Stability of fixed points of Dirac structures. https://doi.org/10.1007/s11005-023-01703-w

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