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Four Steenrod squares on Khovanov homology
Geometry/Topology| Speaker: | Advika Rajapakse, UCLA |
| Related Webpage: | https://www.math.ucla.edu/~advika/ |
| Location: | 2112 MSB |
| Start time: | Tue, Oct 28 2025, 2:10PM |
The Khovanov spectra X_k(L) are a family of spaces, constructed by Sarkar-Scaduto-Stroffregen, that recover even Khovanov homology Kh(L) or odd Khovanov homology Kh_o(L) after taking their cohomology. We investigate these spaces by computing their second Steenrod squares Sq^2. As a result, we uncover four distinct cohomology operations on mod 2 Khovanov homology. We also prove that there exist at least two even Khovanov spectra and two odd Khovanov spectra.