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Creators/Authors contains: "Krannich, Manuel"

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  1. ; ; ; (, 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