G. Peter Scott
Godfrey Peter Scott, known as Peter Scott, 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 with finitely generated fundamental group has a compact core, i.e., is a compact submanifold such that inclusion induces a homotopy equivalence between and ; the submanifold is called a Scott compact core of the manifold. He had previously proved that, given a fundamental group of a 3-manifold, if is finitely generated then 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.Selected publications
- Compact submanifolds of 3-manifolds, Journal of the London Mathematical Society. Second Series vol. 7, no. 2, 246–250
- Finitely generated 3-manifold groups are finitely presented. J. London Math. Soc. Second Series vol. 6, 437–440
- J. London Math. Soc. Second Series vol. 17, no. 3, 555–565.
- * Correction to "Subgroups of surface groups are almost geometric J. London Math. Soc. vol. 2, no. 2, 217–220
- There are no fake Seifert fibre spaces with infinite π1. Ann. of Math. Second Series, vol. 117, no. 1, 35–70
- with Joel Hass and Michael Freedman: Closed geodesics on surfaces, Bull. London Mathematical Society, vol. 14, 1982, 385–391
- with M. Freedman and J. Hass: Least area incompressible surfaces in 3-manifolds. Invent. Math. vol. 71, no. 3, 609–642
- with William H. Meeks: Finite group actions on 3-manifolds. Invent. Math. vol. 86, no. 2, 287–346
- Introduction to 3-Manifolds, University of Maryland, College Park 1975
- The geometries of 3-manifolds, Bulletin London Mathematical Society, vol. 15, 1983, 401–487
- 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, 20–28
