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![5: Film du cobordisme C(b) entre bW (b) et V ert 2n : chaque vignette représente une hauteur différente en commençant par celle en haut à gauche de bW (b) et en terminant en bas à droite par V ert 2n (illustration venant de [Kho02]).](profile/Gregoire-Naisse/publication/283117461/figure/fig4/AS:486713593208834@1493052971715/Film-du-cobordisme-Cb-entre-bW-b-et-V-ert-2n-chaque-vignette-represente-une-hauteur.png)
5: Film du cobordisme C(b) entre bW (b) et V ert 2n : chaque vignette représente une hauteur différente en commençant par celle en haut à gauche de bW (b) et en terminant en bas à droite par V ert 2n (illustration venant de [Kho02]).
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In this master thesis we construct an oddification of the rings $H^n$ from
arXiv:math/0103190 using the functor from arXiv:0710.4300 . This leads to a
collection of non-associative rings $OH^n_C$ where $C$ represent some choices
of signs. Extending the center up to anti-commutative elements, we get a ring
$OZ(OH^n_C)$ which is isomorphic to the odd...
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Citations
... Indeed, all cohomology groups are free and the relation from the Lemma 4.23 gives us the claim since rk(H k (T am )) − rk(H k (T am ∩ T <am )) counts exactly the number of cells of T am \ T <am . Finally, like in [21] (and proved in [27,Lemma 3.64]), the number of cells is 2n n and this concludes the proof. Corollary 4.25. ...
We construct an odd version of Khovanov's arc algebra . 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.
We construct an odd version of Khovanov's arc algebra . 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.
