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1. Non-planar Ends are Continuously Unforgettable

   https://doi.org/10.1093/imrn/rnaf026  

   Aramayona, Javier; de_Pool, Rodrigo; Skipper, Rachel; Tao, Jing; Vlamis, Nicholas G; Wu, Xiaolei (March 2025, International Mathematics Research Notices)

   Abstract We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups. 

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2. Right-angled Artin groups as normal subgroups of mapping class groups

   https://doi.org/10.1112/S0010437X21007417  

   Clay, Matt; Mangahas, Johanna; Margalit, Dan (August 2021, Compositio Mathematica)

   We construct the first examples of normal subgroups of mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non-free right-angled Artin subgroups of other groups, such as braid groups and pure braid groups, as well as many subgroups of the mapping class group, such as the Torelli subgroup. Our work recovers and generalizes the seminal result of Dahmani–Guirardel–Osin, which gives free, purely pseudo-Anosov normal subgroups of mapping class groups. We give two applications of our methods: (1) we produce an explicit proper normal subgroup of the mapping class group that is not contained in any level $$m$$ congruence subgroup and (2) we produce an explicit example of a pseudo-Anosov mapping class with the property that all of its even powers have free normal closure and its odd powers normally generate the entire mapping class group. The technical theorem at the heart of our work is a new version of the windmill apparatus of Dahmani–Guirardel–Osin, which is tailored to the setting of group actions on the projection complexes of Bestvina–Bromberg–Fujiwara. 

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3. Automatic continuity of pure mapping class groups

   Dickmann, R (July 2024, The Womens business resource guide)

   We completely classify the orientable infinite-type surfaces S such that PMap(S), the pure mapping class group, has automatic continuity. This classification includes surfaces with noncompact boundary. In the case of surfaces with finitely many ends and no noncompact boundary components, we prove the mapping class group Map(S) does not have automatic continuity. We also completely classify the surfaces such that PMapc (S), the subgroup of the pure mapping class group composed of elements with representatives that can be approximated by compactly supported homeomorphisms, has automatic continuity. In some cases when PMapc (S) has automatic continuity, we show any homomorphism from PMapc (S) to a countable group is trivial. 

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4. Pseudo-Anosov subgroups of general fibered 3–manifold groups

   https://doi.org/10.1090/btran/157  

   Leininger, Christopher; Russell, Jacob (August 2023, Transactions of the American Mathematical Society, Series B)

   We show that finitely generated and purely pseudo-Anosov subgroups of fundamental groups of fibered 3–manifolds with reducible monodromy are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. Combined with results of Dowdall–Kent–Leininger and Kent–Leininger–Schleimer, this establishes the result for the image of all such fibered 3–manifold groups in the mapping class group. 

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5. Applications of the algebraic geometry of the Putman–Wieland conjecture

   https://doi.org/10.1112/plms.12539  

   Landesman, Aaron; Litt, Daniel (May 2023, Proceedings of the London Mathematical Society)

   Abstract We give two applications of our prior work toward the Putman–Wieland conjecture. First, we deduce a strengthening of a result of Marković–Tošić on virtual mapping class group actions on the homology of covers. Second, let and let be a finite ‐cover of topological surfaces. We show the virtual action of the mapping class group of on an ‐isotypic component of has nonunitary image. 

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