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Higher torsion in the Abelianization of the full Bianchi groups

Alexander Rahm 1, *
* Corresponding author
Abstract : Consider the Bianchi groups, namely the SL_2 groups over rings of imaginary quadratic integers. In the literature, there has been so far no example of p-torsion in the integral homology of the full Bianchi groups, for p a prime greater than the order of elements of finite order in the Bianchi group, which is at most 6. However, extending the scope of the computations, we can observe examples of torsion in the integral homology of the quotient space, at prime numbers as high as for instance p = 80737 at the discriminant -1747.
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Submitted on : Sunday, July 29, 2012 - 7:29:34 PM
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Alexander Rahm. Higher torsion in the Abelianization of the full Bianchi groups. LMS Journal of Computation and Mathematics, London Mathematical Society, 2013, 16, pp. 344 - 365. ⟨10.1112/S1461157013000168⟩. ⟨hal-00721690⟩



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