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• W2907255118 abstract "Let $N$ be a smooth manifold that is homeomorphic but not diffeomorphic to a closed hyperbolic manifold $M$. In this paper, we study the extent to which $N$ admits as much symmetry as $M$. Our main results are examples of $N$ that exhibit two extremes of behavior. On the one hand, we find $N$ with maximal symmetry, i.e. Isom($M$) acts on $N$ by isometries with respect to some negatively curved metric on $N$. For these examples, Isom($M$) can be made arbitrarily large. On the other hand, we find $N$ with little symmetry, i.e. no subgroup of Isom($M$) of small index acts by diffeomorphisms of $N$. The construction of these examples incorporates a variety of techniques including smoothing theory and the Belolipetsky-Lubotzky method for constructing hyperbolic manifolds with a prescribed isometry group." @default.
• W2907255118 created "2019-01-11" @default.
• W2907255118 creator A5063452828 @default.
• W2907255118 creator A5075145457 @default.
• W2907255118 date "2019-01-03" @default.
• W2907255118 modified "2023-09-27" @default.
• W2907255118 title "Symmetries of exotic negatively curved manifolds" @default.
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• W2907255118 hasPublicationYear "2019" @default.
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