A new algorithm for 3-sphere recognition

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.

8 pages, comments are welcome! v2: misspellings corrected

References in corpus (2)

• Integer homology 3-spheres admit irreducible representations in SL(2,C)
• Recognizing geometric 3-manifold groups using the word problem

Cited by in corpus (1)

• Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation