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Creators/Authors contains: "Tshishiku, Bena"

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  1. ; ; (, Groups, Geometry, and Dynamics)
    For each circle bundleS^{1}\to X\to\Sigma_{g}over a surface with genusg\ge2, there is a natural surjection\pi:\operatorname{Homeo}^{+}(X)\to\operatorname{Mod}(\Sigma_{g}). WhenXis the unit tangent bundleU\Sigma_{g}, it is well known that\pisplits. On the other hand,\pidoes not split when the Euler numbere(X)is not divisible by the Euler characteristic\chi(\Sigma_{g})by Chen and Tshishiku (2023). In this paper, we show that this homomorphism does not split in many cases where\chi(\Sigma_{g})dividese(X). 
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    Free, publicly-accessible full text available May 29, 2026
  2. ; ; ; (, Transactions of the American Mathematical Society, Series B)
    We determine for which exotic tori T \mathcal {T} of dimension d ≠<#comment/> 4 d\neq 4 the homomorphism from the group of isotopy classes of orientation-preserving diffeomorphisms of T \mathcal {T} to S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) given by the action on the first homology group is split surjective. As part of the proof we compute the mapping class group of all exotic tori T \mathcal {T} that are obtained from the standard torus by a connected sum with an exotic sphere. Moreover, we show that any nontrivial S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) -action on T \mathcal {T} agrees on homology with the standard action, up to an automorphism of S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) . When combined, these results in particular show that many exotic tori do not admit any nontrivial differentiable action by S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) . 
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    Free, publicly-accessible full text available November 15, 2025
  3. ; (, Michigan Mathematical Journal)
    Abstract. In this paper, we study the algebraic structure of mapping class group Mod(X) of 3-manifolds X that fiber as a circle bundle over a surface S1 → X → Sg. There is an exact sequence 1→H1(Sg)→Mod(X)→Mod(Sg)→1. We relate this to the Birman exact sequence and determine when this sequence splits. 
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  4. ; (, Groups, Geometry, and Dynamics)
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  5. ; ; (, Tunisian Journal of Mathematics)
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  6. ; (, Groups, Geometry, and Dynamics)
    null (Ed.)
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  7. ; (, Compositio Mathematica)
    A question of Griffiths–Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for a class of algebraic surfaces known as Atiyah–Kodaira manifolds, which have base and fibers equal to complete algebraic curves. Our methods are topological in nature and involve an analysis of the ‘geometric’ monodromy, valued in the mapping class group of the fiber. 
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