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   https://doi.org/10.1112/jlms.70093  

   Lafont, Jean‐François; Ruffoni, Lorenzo (April 2025, Journal of the London Mathematical Society)

   Abstract We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non‐positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non‐triangulable aspherical manifolds with virtually special fundamental group. 

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2. Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations

   https://doi.org/10.1215/00127094-2021-0003  

   Fakhruddin, Najmuddin; Khare, Chandrashekhar; Patrikis, Stefan (November 2021, Duke Mathematical Journal)
3. K-theory of relative group C*-algebras and the relative Novikov conjecture

   https://doi.org/10.1007/s00209-024-03439-2  

   Deng, Jintao; Tian, Geng; Xie, Zhizhang; Yu, Guoliang (March 2024, Mathematische Zeitschrift)
4. K-theory of relative group C∗-algebras and the relative Novikov conjecture

   Deng, Jintao; Tian, Geng; Xie, Zhizhang; Yu, Guoliang (February 2024, Mathematische Zeitschrift)

   The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. The relative Baum–Connes assembly encodes information about the relative higher index of elliptic operators on manifolds with boundary. In this paper, we study the relative Baum– Connes assembly map for any pair of groups and apply it to solve the relative Novikov conjecture when the groups satisfy certain geometric conditions. 

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5. Relative Error Streaming Quantiles

   https://doi.org/10.1145/3452021.3458323  

   Cormode, Graham; Karnin, Zohar; Liberty, Edo; Thaler, Justin; Veselý, Pavel (June 2021, PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems)

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