G. Peter Scott

Godfrey Peter Scott, known as Peter Scott, (born 1944) is a British mathematician, known for the Scott core theorem.

Scott received his PhD in 1969 from the University of Warwick under Brian Joseph Sanderson. Scott was a professor at the University of Liverpool and later at the University of Michigan.

His research deals with low-dimensional geometric topology, differential geometry, and geometric group theory. He has done research on the geometric topology of 3-dimensional manifolds, 3-dimensional hyperbolic geometry, minimal surface theory, hyperbolic groups, and Kleinian groups with their associated geometry, topology, and group theory.

In 1973 he proved what is now known as the Scott core theorem or the Scott compact core theorem. This states that every 3-manifold ${\displaystyle M}$ with finitely generated fundamental group has a compact core ${\displaystyle N}$, i.e., ${\displaystyle N}$ is a compact submanifold such that inclusion induces a homotopy equivalence between ${\displaystyle N}$ and ${\displaystyle M}$; the submanifold ${\displaystyle N}$ is called a Scott compact core of the manifold ${\displaystyle M}$. He had previously proved that, given a fundamental group ${\displaystyle G}$ of a 3-manifold, if ${\displaystyle G}$ is finitely generated then ${\displaystyle G}$ must be finitely presented.

In 1986 he was awarded the Senior Berwick Prize. in 2012 he was elected a Fellow of the American Mathematical Society.

• Compact submanifolds of 3-manifolds, Journal of the London Mathematical Society. Second Series vol. 7 (1973), no. 2, 246–250 (proof of the theorem on the compact core) doi:10.1112/jlms/s2-7.2.246
• Finitely generated 3-manifold groups are finitely presented. J. London Math. Soc. Second Series vol. 6 (1973), 437–440 doi:10.1112/jlms/s2-6.3.437
• Subgroups of surface groups are almost geometric. J. London Math. Soc. Second Series vol. 17 (1978), no. 3, 555–565. (proof that surface groups are LERF) doi:10.1112/jlms/s2-17.3.555
  • Correction to "Subgroups of surface groups are almost geometric J. London Math. Soc. vol. 2 (1985), no. 2, 217–220 doi:10.1112/jlms/s2-32.2.217
• There are no fake Seifert fibre spaces with infinite π₁. Ann. of Math. Second Series, vol. 117 (1983), no. 1, 35–70 doi:10.2307/2006970
• with Joel Hass and Michael Freedman: Closed geodesics on surfaces, Bull. London Mathematical Society, vol. 14, 1982, 385–391 doi:10.1112/blms/14.5.385
• with M. Freedman and J. Hass: Least area incompressible surfaces in 3-manifolds. Invent. Math. vol. 71 (1983), no. 3, 609–642 doi:10.1007/BF02095997
• with William H. Meeks: Finite group actions on 3-manifolds. Invent. Math. vol. 86 (1986), no. 2, 287–346 doi:10.1007/BF01389073
• Introduction to 3-Manifolds, University of Maryland, College Park 1975
• The geometries of 3-manifolds, Bulletin London Mathematical Society, vol. 15, 1983, 401–487 doi:10.1112/blms/15.5.401 pdf
• with Gadde A. Swarup: Regular neighbourhoods and canonical decompositions for groups, Société Mathématique de France, 2003
  • Regular neighbourhoods and canonical decompositions for groups, Electron. Res. Announc. Amer. Math. Soc. vol. 8 (2002), 20–28 doi:10.1090/S1079-6762-02-00102-6