  We prove the existence of a new algorithm for 3-sphere recognition based on
Groebner basis methods applied to the variety of $\text{\em
SL}(2,\C)$-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 $\text{\em SL}(2,\C)$. This result, and hence our
algorithm, build on the geometrisation theorem of 3-manifolds.
