2
$\begingroup$

Szabo equipped the mod $2$ Khovanov complex with a family of differentials $\{d_{i} \}_{i=1}^{\infty}$ such that each $d_{i}$ has bigrading $(i,2i-2)$ where $d_1$ is the mod $2$ Khovanov differential and $\delta_{Sz}=\sum_{i=1}^{n}d_i$ is the total differential in https://arxiv.org/abs/1010.4252v2. He defined a spectral $\{E_{i} \}$ sequence using the homological filtration of the Khovanov complex.
We notice that the quantum grading in each $d_i$ is also increasing. So, there is an another spectral sequence $\{E^{'}_{i} \}$ using quantum filtration as well.

Question: Are the two spectral sequences isomorphic? My hunch is $E_{i+1}=E^{'}_{i}$. This is because the first spectral sequence picks up the Khovanov homology at the second page but however the second one picks it up at the first page. How about the subsequent pages?

I will really appreciate any comment on this. Thank you!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.