Peter Shalen

Peter Shalen

Peter B. Shalen is an American mathematician, working primarily in low-dimensional topology. He is the "S" in JSJ decomposition.

Life

He graduated from Stuyvesant High School in 1962, [cite web |url=http://65.104.11.121/MathTeam.html |title=Stuyvesant Math Team |accessdate=2007-10-31] and went on to earn an undergraduate degree in 1966 and his Ph.D. in 1972, both from Harvard University. After posts at Columbia University, Rice University, and the Courant Institute, he joined the faculty of the University of Illinois at Chicago, where he currently has seven mathematical descendants.

Work

His work with Marc Culler related properties of representation varieties of hyperbolic 3-manifold groups to decompositions of 3-manifolds. Based on this work, Culler, Cameron Gordon, John Luecke, and Shalen proved the cyclic surgery theorem. An important corollary of the theorem is that at most one nontrivial Dehn surgery (+1 or −1) on a knot can result in a simply-connected 3-manifold. This was an important piece of the Gordon-Luecke theorem that knots are determined by their complements. This paper is often referred to as "CGLS".

With John W. Morgan, he generalized his work with Culler, and reproved several foundational results of William Thurston.

elected publications

*cite book | author=Jaco, William H. and Shalen, Peter B. | title=Seifert fibered spaces in 3-manifolds | location=Providence | publisher=American Mathematical Society | year=1979 | id=ISBN 0-8218-2220-9
*Shalen, Peter B. "Separating, incompressible surfaces in 3-manifolds." Invent. Math. 52 (1979), no. 2, 105–126.
* Culler, Marc; Shalen, Peter B. "Varieties of group representations and splittings of 3-manifolds." Ann. of Math. (2) 117 (1983), no. 1, 109–146.
* Culler, Marc; Gordon, C. McA.; Luecke, J.; Shalen, Peter B. "Dehn surgery on knots." Ann. of Math. (2) 125 (1987), no. 2, 237–300.
* Morgan, John W.; Shalen, Peter B. "Valuations, trees, and degenerations of hyperbolic structures. I." Ann. of Math. (2) 120 (1984), no. 3, 401–476.
* Morgan, John W.; Shalen, Peter B. "Degenerations of hyperbolic structures. II. Measured laminations in 3-manifolds." Ann. of Math. (2) 127 (1988), no. 2, 403–456.
* Morgan, John W.; Shalen, Peter B. "Degenerations of hyperbolic structures. III. Actions of 3-manifold groups on trees and Thurston's compactness theorem." Ann. of Math. (2) 127 (1988), no. 3, 457–519.

References

External links

* [http://www.math.uic.edu/~shalen/ Shalen's home page at UIC]
* [http://65.104.11.121/MathTeam.html Art Rothstein's Stuyvesant Math Team page]
* [http://www.genealogy.ams.org/html/id.phtml?id=33560 Peter Shalen's mathematical genealogy]


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Marc Culler — Photograph by Roberta Devlin Born November 22, 1953 …   Wikipedia

  • JSJ decomposition — In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: Irreducible orientable closed (i.e., compact and without boundary) 3 manifolds have a unique (up to isotopy)… …   Wikipedia

  • JSJ-Zerlegung — Die Jaco Shalen Johannson Zerlegung, abgekürzt JSJ Zerlegung, benannt nach William Jaco, Peter Shalen und Klaus Johannson, ist eine Aussage aus der Topologie der 3 Mannigfaltigkeiten. Aussage Sie besagt, dass jede 3 dimensionale Mannigfaltigkeit… …   Deutsch Wikipedia

  • Fibré de Seifert — En topologie, un fibré de Seifert est une variété de dimension 3 munie d une « bonne » partition en cercles. Plus précisément, c est un fibré en cercles sur un orbifold de dimension 2. Ces variétés ont été introduites par Herbert… …   Wikipédia en Français

  • Seifert-Faserung — In der dreidimensionalen Topologie versteht man unter einer Seifert Faserung eine dreidimensionale Mannigfaltigkeit, die auf eine bestimmte Weise durch Kreise gefasert ist. Eine solche Seifert gefaserte Mannigfaltigkeit lässt sich als Vereinigung …   Deutsch Wikipedia

  • Cyclic surgery theorem — In three dimensional topology, a branch of mathematics, the cyclic surgery theorem states that, for a compact, connected, orientable, irreducible three manifold M whose boundary is a torus T, if M is not a Seifert fibered space and r,s are slopes …   Wikipedia

  • List of Stuyvesant High School people — This article lists notable people associated with Stuyvesant High School in New York City, New York, organized into rough professional areas and listed in order by their graduating class. MathematicsStuyvesant High School has produced a steady… …   Wikipedia

  • History of knot theory — For thousands of years, knots have been used for basic purposes such as recording information, fastening and tying objects together. Over time people realized that different knots were better at different tasks, such as climbing or sailing. Knots …   Wikipedia

  • Triangulation (topology) — In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K , homeomorphic to X , together with a homeomorphism h : K o X . Triangulation is… …   Wikipedia

  • Cameron Gordon (mathematician) — Cameron Gordon is a professor of mathematics at the University of Texas at Austin, known for his work in knot theory. Among his notable results is his work with Marc Culler, John Luecke, and Peter Shalen on the cyclic surgery theorem. This was an …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”