We prove the existence of a new algorithm for 3-sphere recognition based on Groebner basis methods applied to the variety of SL(2,)-representation of the fundamental group. An essential input is a recent result of the second author, stating that any integer homology 3-sphere different from the 3-sphere admits an irreducible representation of its fundamental group in SL(2,). This result, and hence our algorithm, build on the geometrisation theorem of 3-manifolds.
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