Michael Heusener, Raphael Zentner
Published 2016-10-13Version 1
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.
Comments: 8 pages, comments are welcome
Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds
Three manifold groups, Kaehler groups and complex surfaces
Structure of the fundamental groups of orbits of smooth functions on surfaces
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