# Superfiltered $A_\infty$-deformations of the exterior algebra, and local mirror symmetry

@inproceedings{Smith2019SuperfilteredO, title={Superfiltered \$A_\infty\$-deformations of the exterior algebra, and local mirror symmetry}, author={Jack Smith}, year={2019} }

The exterior algebra $E$ on a finite-rank free module $V$ carries a $\mathbb{Z}/2$-grading and an increasing filtration, and the $\mathbb{Z}/2$-graded filtered deformations of $E$ as an associative algebra are the familiar Clifford algebras, classified by quadratic forms on $V$. We extend this result to $A_\infty$-algebra deformations $\mathcal{A}$, showing that they are classified by formal functions on $V$. The proof translates the problem into the language of matrix factorisations, using the… CONTINUE READING

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