[PHK_seminar] [Cohomology]Wednesday 13 May, Malkhaz Bakuradze

[Igor Khavkine]

Dear All,

The video recording of the talk by Malkhaz Bakuradze from last week is 
now available on YouTube at

   https://youtu.be/anVgptphdxc

The slides are available from

   https://users.math.cas.cz/~hvle/PHK/BakuradzeBredoncohomology2026.pdf

Both links have also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/160/

Best,

Igor

On 5/11/26 1:00 PM, sender of seminar announcement via phk_seminar wrote:
> Wednesday, 13 May 2026 - 13:30 to 14:30
> Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, the blue 
> lecture room + ZOOM meeting
> 
> Speaker: Malkhaz Bakuradze, Iv. Javakhishvili Tbilisi State University
> Title: On Equivariant Bredon Cohomologies with Maskey Functor in Morava 
> K-theory
> 
> Abstract
> 
> Abstract in the attached pdf file. Here is a latex transcription.
> 
> 
> Our consideration of the Mackey functor $\underline{M}$ for Bredon 
> cohomology relies on the explicit Morava K-theory ring calculations for 
> ’good’ finite p-groups provided in [Bakuradze, M. Morava K-theory rings 
> for finite groups. J. Homotopy Relat. Struct. 20, 567–630 (2025)]
> 
> 
> Let $G$ be a finite group and $X$ a finite $G$-CW complex. We define the 
> contravariant Bredon $\underline{K(n)}^*$ module on the orbit category $ 
> \mathcal{O}_G$ by setting $M(G/H) = K(n)^*(BH)$ for each subgroup $H 
> \subseteq G$. The $n$-th Bredon cochain group is defined as the direct 
> sum over the $n$-dimensional orbit representatives:
> 
>    \[ C_G^n(X; \underline{K(n)}^*) = \bigoplus_{\sigma \in \text{Orbits} 
> _n(X)} K(n)^*(BG_\sigma) \]
> 
>    The coboundary operator $\delta^n: C_G^n \to C_G^{n+1}$ is given by:
> 
>    \[ (\delta^n \alpha)(\psi) = \sum_{\sigma \in \text{Orbits}_n} 
> \sum_{g \in G} [\psi : g\sigma] \cdot \text{Res}_{G_\psi}^{gG_\sigma 
> g^{-1}}(\alpha_\sigma) \]
> 
>    where $[\psi : g\sigma]$ are the degrees of the corresponding 
> attaching maps and $\text{Res}$ is the restriction map in Morava $K$- 
> theory. The $n$-th Bredon cohomology group of $X$ with coefficients in $ 
> \underline{K(n)}^*$ is:
> 
>    \[ H_G^n(X; \underline{K(n)}^*) = \frac{\ker(\delta^n)}{\text{im} 
> (\delta^{n-1})} \]
> 
>    While the evenness of the Bredon cohomology is a sufficient rather 
> than a necessary criterion for the goodness of $X$, it remains the most 
> computationally viable path. If this $E_2$-condition is met, the 
> equivariant Atiyah-Hirzebruch spectral sequence collapses immediately.
> 
> -----------------------------------------------------------------------------------------------
> 
> We shall open the seminar room and ZOOM meeting at 13.15 for coffee and 
> close ZOOM at 15.30
> 
> 
> Join Zoom Meeting
> 
> 
> https://cesnet.zoom.us/j/99598413922? 
> pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09 <https://cesnet.zoom.us/ 
> j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09>
> 
> 
> Meeting ID:99598413922
> 
> Passcode:Galois
> 
> -----------------------------------------------------
> 
> On May 20 Igor Khavkine shall give a talk Compatibility complex for the 
> conformal-to-Einstein operator <https://www.math.cas.cz/index.php/ 
> events/event/4137>
> 
> 
> 
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
> 
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
> 
> 
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