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Real Springer fibers and odd arc algebras

MPS-Authors
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Eberhardt,  Jens Niklas
Max Planck Institute for Mathematics, Max Planck Society;

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Naisse,  Grégoire
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource
Fulltext (public)

arXiv:2003.07297.pdf
(Preprint), 485KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Eberhardt, J. N., Naisse, G., & Wilbert, A. (in press). Real Springer fibers and odd arc algebras. Journal of the London Mathematical Society, Early view Online - Print pending. doi:10.1112/jlms.12413.


Cite as: http://hdl.handle.net/21.11116/0000-0007-A100-2
Abstract
We give a topological description of the two-row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda-Russell. We also realize Ozsv\'ath-Rasmussen-Szab\'o odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we construct the odd arc algebra as a convolution algebra over components of the real Springer fiber, giving an odd analogue of a construction of Stroppel-Webster.