Odd Khovanov's arc algebra

Abstract

We construct an odd version of Khovanov's arc algebra $H^n$. Extending the center to elements that anticommute, we get a subalgebra that is isomorphic to the oddification of the cohomology of the $(n,n)$-Springer varieties. We also prove that the odd arc algebra can be twisted into an associative algebra.

arXiv comment34 pages. v3 with new subsection "proof of theorem 4.1" giving more details on the proof of this result and a bunch of miscellaneous corrections