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On Jordan type bounds for finite groups acting on compact 3-manifolds

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Abstract

By a classical result of Jordan, each finite subgroup of a complex linear group \({{\rm GL}_n(\mathbb{C})}\) has an abelian normal subgroup whose index is bounded by a constant depending only on n. It has been asked whether this remains true for finite subgroups of the diffeomorphism group Diff(M) of every compact manifold M; in the present paper, using the geometrization of 3-manifolds, we prove it for compact 3-manifolds M.

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  1. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, 34127, Trieste, Italy

    Bruno P. Zimmermann

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  1. Bruno P. Zimmermann
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Zimmermann, B.P. On Jordan type bounds for finite groups acting on compact 3-manifolds. Arch. Math. 103, 195–200 (2014). https://doi.org/10.1007/s00013-014-0671-z

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