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Award ID contains: 1904913

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  1. ; ; (, Geometric and Functional Analysis)
    Abstract We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3–manifolds and answer questions of Agol–Liu (J. Am. Math. Soc. 25(1):151–187, 2012) and Reid–Wang–Zhou (Acta Math. Sin. Engl. Ser. 18(1):157–172, 2002). 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; (, Journal of the Institute of Mathematics of Jussieu)
    Abstract Let M be an irreducible $$3$$ -manifold M with empty or toroidal boundary which has at least one hyperbolic piece in its geometric decomposition, and let A be a finite abelian group. Generalizing work of Sun [20] and of Friedl–Herrmann [7], we prove that there exists a finite cover $$M' \to M$$ so that A is a direct factor in $$H_1(M',{\mathbb Z})$$ . 
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  3. ; (, Journal of Topology)
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  4. ; (, Bulletin of the London Mathematical Society)
    Italiano–Martelli–Migliorini recently constructed hyperbolic groups which have non-hyperbolic subgroups of finite type. Using a closely related construction, Llosa Isenrich–Martelli–Py constructed hyperbolic groups with subgroups of type F3 but not F4. We observe that these hyperbolic groups can be chosen to be special in the sense of Haglund–Wise. 
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  5. ; (, Journal of the London Mathematical Society)
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  6. ; (, 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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  7. ; (, Compositio Mathematica)
    null (Ed.)
    We introduce a new kind of action of a relatively hyperbolic group on a $$\text{CAT}(0)$$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case. 
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