Dehn twists along (-2)-spheres on K3-type 4-manifolds are not homotopy coherently Nielsen realizable, as shown via family Seiberg-Witten theory.
Non-trivial smooth families ofK3surfaces
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Fibrewise orbifold resolutions produce bundles inducing free subgroups in π₂ of relative homotopy automorphism spaces, applied to exhibit positive-rank free subgroups in G₂ moduli spaces.
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Homotopy Coherent Nielsen Realization Problem for Dehn Twists on K3-Type 4-Manifolds
Dehn twists along (-2)-spheres on K3-type 4-manifolds are not homotopy coherently Nielsen realizable, as shown via family Seiberg-Witten theory.
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Fibrewise Orbifold Resolutions with Applications to $\mathrm{G}_2$-Moduli Spaces
Fibrewise orbifold resolutions produce bundles inducing free subgroups in π₂ of relative homotopy automorphism spaces, applied to exhibit positive-rank free subgroups in G₂ moduli spaces.