A new algorithm for 3-sphere recognition

Michael Heusener; Raphael Zentner

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arXiv · 1610.04092

A new algorithm for 3-sphere recognition

Michael Heusener·Raphael Zentner

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Abstract

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.

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Michael Heusener, Raphael Zentner. 2016-10-13. A new algorithm for 3-sphere recognition. https://arxiv.org/abs/1610.04092

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