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Torsion growth for Bianchi groups

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Bianchi groups, e.g. SL2(Z[i]), are natural generalizations of the classical modular group SL2(Z). Motivated by recent developments in the Langlands programme, we consider the size of torsion in the abelianization of finite index subgroups of Bianchi groups. After giving some background and motivation, we shall discuss joint work with Akshay Venkatesh (Stanford) and Nicolas Bergeron (Paris 6) which shows that under suitable hypotheses the size of torsion grows exponentially with respect to the index. The main tool is the celebrated Cheeger-Mueller theorem from global analysis which essentially asserts the equality of topological and analytical torsions.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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