Scott core theorem

In mathematics, the Scott core theorem is a theorem about the finite presentability of fundamental groups of 3-manifolds due to G. Peter Scott. The precise statement is as follows:

Given a 3-manifold (not necessarily compact) with finitely generated fundamental group, there is a compact three-dimensional submanifold, called the compact core or Scott core, such that its inclusion map induces an isomorphism on fundamental groups. In particular, this means a finitely generated 3-manifold group is finitely presentable.

References

• Rubinstein, J. H.; Swarup, G. A. (1990), "On Scott's core theorem", The Bulletin of the London Mathematical Society, 22 (5): 495–498, doi:10.1112/blms/22.5.495, ISSN 0024-6093, MR1082023
• Scott, G. P. (1973), "Compact submanifolds of 3-manifolds", Journal of the London Mathematical Society. Second Series, 7: 246–250, doi:10.1112/jlms/s2-7.2.246, ISSN 0024-6107, MR0326737