G. Peter Scott
{{Short description|British mathematician}}
{{Use dmy dates|date=April 2022}}
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| birth_name = Godfrey Peter Scott
| birth_date = {{birth year|1944}}
| birth_place = England
| death_date = {{death date and age |2023|09|19|1944}}
| death_place = Michigan, United States
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| other_names = Peter Scott
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| fields = Mathematics
| workplaces = University of Liverpool
University of Michigan
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| alma_mater = University of Oxford
University of Warwick
| thesis_title = Some Problems in Topology
| thesis_url = https://wrap.warwick.ac.uk/61719/1/WRAP_THESIS_Scott_1968.pdf
| thesis_year = 1969
| doctoral_advisor = Brian Joseph Sanderson
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| known_for = Scott core theorem
| awards = Senior Berwick Prize
Fellow of the American Mathematical Society
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Godfrey Peter Scott, known as Peter Scott, (1944 – 19 September 2023) was a British-American mathematician, known for the Scott core theorem.
Education and career
He was born in England to Bernard Scott (a mathematician) and Barbara Scott (a poet and sculptor). After completing his BA at the University of Oxford, Peter Scott received his PhD in 1969 from the University of Warwick under Brian Joseph Sanderson, with thesis Some Problems in Topology.{{MathGenealogy|id=7934|title=G. Peter "Godfrey" Scott}} Scott held appointments at the University of Liverpool from 1968 to 1987, at which time he moved to the University of Michigan, where he was a professor until his retirement in 2018.
His research dealt 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 .{{cite book|author=Kapovich, Michael|authorlink=Michael Kapovich|title=Hyperbolic Manifolds and Discrete Groups|year=2009|page=113|url=https://books.google.com/books?id=JRJ8VmfP-hcC&pg=PA113|isbn=9780817649135}} He had previously proved that, given a fundamental group of a 3-manifold, if is finitely generated then must be finitely presented.
Awards and honours
In 1986, he was awarded the Senior Berwick Prize by the London Mathematical Society. In 2013, he was elected a Fellow of the American Mathematical Society.{{cite web|url=http://www.ams.org/cgi-bin/fellows/fellows.cgi|title=List of Fellows of the American Mathematical Society|publisher=American Mathematical Society|access-date=2 December 2023}}
Death
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) {{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}}
- [https://academic.oup.com/jlms/article-abstract/s2-17/3/555/903467?redirectedFrom=PDF 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. Annals of Mathematics Second Series, vol. 117 (1983), no. 1, 35–70 {{doi|10.2307/2006970}}
- {{Cite journal|last1=Freedman|first1=Michael|author1-link=Michael Freedman|last2=Hass|first2=Joel|author2-link=Joel Hass|last3=Scott|first3=Peter|year=1982|title=Closed geodesics on surfaces|journal=Bulletin of the London Mathematical Society|volume=14|issue=5|pages=385–391|doi=10.1112/blms/14.5.385}}
- {{Cite journal|last1=Freedman|first1=Michael|author1-link=Michael Freedman|last2=Hass|first2=Joel|author2-link=Joel Hass|last3=Scott|first3=Peter|year=1983|title=Least area incompressible surfaces in 3-manifolds|journal=Inventiones Mathematicae|volume=71|issue=3|pages=609–642|doi=10.1007/BF02095997|bibcode=1983InMat..71..609F |hdl=2027.42/46610|s2cid=42502819|hdl-access=free}}
- 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
- {{Cite journal|last=Scott|first=Peter|year=1983|title=The Geometries of 3-Manifolds|journal=Bulletin of the London Mathematical Society|volume=15|issue=5|pages=401–487|doi=10.1112/blms/15.5.401|url=http://www.math.lsa.umich.edu/~pscott/8geoms.pdf|hdl=2027.42/135276|hdl-access=free}}
- with Gadde A. Swarup: Regular neighbourhoods and canonical decompositions for groups, Société Mathématique de France, 2003
- with Gadde A. Swarup: 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}}
References
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Category:20th-century English mathematicians
Category:21st-century English mathematicians
Category:Alumni of the University of Oxford
Category:Alumni of the University of Warwick
Category:Academics of the University of Liverpool
Category:University of Michigan faculty