Simon-type conjecture for knot exteriors in rational homology spheres

Let XX be a knot exterior in a closed orientable 33-manifold such that H1(X;Q)QH_1(X;\mathbf{Q})\cong\mathbf{Q}. Simon-type knot-exterior conjecture. Then π1(X)\pi_1(X) surjects onto only finitely many groups π1(Xi)\pi_1(X_i), where each XiX_i is a knot exterior satisfying H1(Xi;Q)QH_1(X_i;\mathbf{Q})\cong\mathbf{Q}. This is presented as another natural extension of Simon's conjecture; the supplied text provides no proof or resolution, so the assertion remains open.

Sources & referencesView supporting material

Primary source

Michel Boileau, Steve Boyer, Alan W. Reid and Shicheng Wang, “Simon's conjecture for 2-bridge knots”, arXiv:0903.2898 (2009).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.