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arXiv · 1512.07959

Realizing congruence subgroups inside the diffeomorphism group of a product of homotopy spheres

Somnath Basu·Thomas Farrell
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Abstract

Let M be a smooth manifold which is homeomorphic to the n-fold product of S^k, where k is odd. There is an induced homomorphism from the group of diffeomorphisms of M to the automorphism group of H k (M ; Z). We prove that the image of this homomorphism contains a congruence subgroup of SL_n (Z) whenever n is at least 3.

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Somnath Basu, Thomas Farrell. 2015-12-25. Realizing congruence subgroups inside the diffeomorphism group of a product of homotopy spheres. https://arxiv.org/abs/1512.07959

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