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1. Property G and the 4-genus

   https://doi.org/10.1090/btran/153  

   Ni, Yi (January 2024, Transactions of the American Mathematical Society, Series B)

   We say a null-homologous knot $K$in a $3$-manifold $Y$has Property G, if the Thurston norm and fiberedness of the complement of $K$is preserved under the zero surgery on $K$. In this paper, we will show that, if the smooth $4$-genus of $K\times <\#comment/>\left\{0\right\}$(in a certain homology class) in $(Y\times <\#comment/>[0,1\left]\right)\mathrm{\#<\#comment/>}N\stackrel{¯<\#comment/>}{\mathbb{C}{P}^2}$, where $Y$is a rational homology sphere, is smaller than the Seifert genus of $K$, then $K$has Property G. When the smooth $4$-genus is $0$, $Y$can be taken to be any closed, oriented $3$-manifold. 

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2. Elmendorf constructions for $$G$$-categories and $$G$$-posets

   https://doi.org/10.1090/proc/15563  

   Rubin, Jonathan (September 2021, Proceedings of the American Mathematical Society)
3. The G-stable rank for tensors and the cap setproblem

   https://doi.org/10.2140/ant.2022.16.1071  

   Derksen, Harm (January 2022, Algebra & Number Theory)
4. Local types of (Γ,G)$$(\Gamma ,G)$$‐bundles and parahoric group schemes

   https://doi.org/10.1112/plms.12544  

   Damiolini, Chiara; Hong, Jiuzu (June 2023, Proceedings of the London Mathematical Society)

   Abstract Let be a simple algebraic group over an algebraically closed field . Let be a finite group acting on . We classify and compute the local types of ‐bundles on a smooth projective ‐curve in terms of the first nonabelian group cohomology of the stabilizer groups at the tamely ramified points with coefficients in . When , we prove that any generically simply connected parahoric Bruhat–Tits group scheme can arise from a ‐bundle. We also prove a local version of this theorem, that is, parahoric group schemes over the formal disc arise from constant group schemes via tamely ramified coverings. 

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5. The moduli space of G-algebras

   https://doi.org/10.1016/j.aim.2023.109240  

   O'Desky, Andrew; Rosen, Julian (August 2023, Advances in Mathematics)