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1. A census of exceptional Dehn fillings

   https://doi.org/10.7910/DVN/6WNVG0  

   Dunfield, Nathan (January 2018, Harvard Dataverse)

   This dataset gives the complete list of all 205,822 exceptional Dehn fillings on the 1-cusped hyperbolic 3-manifolds that have ideal triangulations with at most 9 ideal tetrahedra. 

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2. Dehn functions and Hölder extensions in asymptotic cones

   https://doi.org/10.1515/crelle-2018-0041  

   Lytchak, Alexander; Wenger, Stefan; Young, Robert (January 2019, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying according to the type of disc used. In this paper, we introduce a new definition of the Dehn function and use it to prove several theorems. First, we generalize the quasi-isometry invariance of the Dehn function to a broad class of spaces. Second, we prove Hölder extension properties for spaces with quadratic Dehn function and their asymptotic cones. Finally, we show that ultralimits and asymptotic cones of spaces with quadratic Dehn function also have quadratic Dehn function. The proofs of our results rely on recent existence and regularity results for area-minimizing Sobolev mappings in metric spaces. 

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3. Quasiconvexity and Dehn filling

   https://doi.org/10.1353/ajm.2021.0007  

   Groves, Daniel; Manning, Jason Fox (January 2021, American Journal of Mathematics)

   We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with recent work of Cooper and Futer, we provide a new proof of the virtual fibering of non-compact finite-volume hyperbolic 3-manifolds, a result first proved by Wise. Additionally, we explain how previous results on multiplicity and height can be generalized to the relative setting to control the relative height of relatively quasiconvex subgroups under appropriate Dehn fillings. 

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4. Conjugacy problem in groups with quadratic Dehn function

   https://doi.org/10.1142/S1664360719500231  

   Olshanskii, A. Yu.; Sapir, M. V. (April 2020, Bulletin of Mathematical Sciences)

   null (Ed.)

   We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem. This solves Rips’ problem formulated in 1994. 

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5. On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling

   https://doi.org/10.1090/proc/16086  

   Di Cerbo, Luca; Golla, Marco (January 2023, Proceedings of the American Mathematical Society)

   We show that the complex-hyperbolic Einstein Dehn filling compactification cannot possibly be performed in dimension four. 

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