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

arxiv: 1512.07959 · v1 · pith:REVZACUAnew · submitted 2015-12-25 · 🧮 math.AT · math.KT

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

Somnath Basu , Thomas Farrell This is my paper

classification 🧮 math.AT math.KT

keywords groupcongruencehomomorphismproductautomorphismcontainsdiffeomorphismdiffeomorphisms

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

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