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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 , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020 ...
under Brian Joseph Sanderson. Scott was a professor at the
University of Liverpool , mottoeng = These days of peace foster learning , established = 1881 – University College Liverpool1884 – affiliated to the federal Victoria Universityhttp://www.legislation.gov.uk/ukla/2004/4 University of Manchester Act 200 ...
and later at the
University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...
. 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 In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces tha ...
theory,
hyperbolic group In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a ''word hyperbolic group'' or ''Gromov hyperbolic group'', is a finitely generated group equipped with a word metric satisfying certain properties abstra ...
s, and
Kleinian group In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space . The latter, identifiable with , is the quotient group of the 2 by 2 complex matrices of determinant 1 by their ...
s 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 In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...
M with finitely generated fundamental group has a compact core N, ''i.e.'', N is a
compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in Britis ...
submanifold In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which ...
such that inclusion induces a
homotopy equivalence In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a defo ...
between N and M; the submanifold N is called a ''Scott compact core'' of the manifold M. He had previously proved that, given a fundamental group G of a 3-manifold, if G is finitely generated then G must be finitely presented. In 1986, he was awarded the
Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...
. In 2012, he was elected a Fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...
.


Selected publications

* ''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) * ''Finitely generated 3-manifold groups are finitely presented.'' J. London Math. Soc. Second Series vol. 6 (1973), 437–440
''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) ** ''Correction to "Subgroups of surface groups are almost geometric'' J. London Math. Soc. vol. 2 (1985), no. 2, 217–220 * ''There are no fake Seifert fibre spaces with infinite π1.'' Ann. of Math. Second Series, vol. 117 (1983), no. 1, 35–70 * * * with William H. Meeks: ''Finite group actions on 3-manifolds.'' Invent. Math. vol. 86 (1986), no. 2, 287–346 *''Introduction to 3-Manifolds'', University of Maryland, College Park 1975 * *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


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{{DEFAULTSORT:Scott, G Peter 20th-century English mathematicians 21st-century English mathematicians Alumni of the University of Warwick Academics of the University of Liverpool University of Michigan faculty Fellows of the American Mathematical Society 1945 births Living people Topologists Group theorists