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Peter B. Shalen (born c. 1946) is an American mathematician , working primarily in low-dimensional topology . He is the "S" in JSJ decomposition .
Life
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He graduated from Stuyvesant High School in 1962,[1] and went on to earn a B.A. from Harvard College in 1966 and his Ph.D. from Harvard University in 1972.[2] After posts at Columbia University , Rice University , and the Courant Institute , he joined the faculty of the University of Illinois at Chicago .
Shalen was a Sloan Foundation Research Fellow in mathematics (1977—1979).[3] In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California .[4] He was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to three-dimensional topology and for exposition".[5]
Work
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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 .
Selected publications
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Jaco, William H. & Shalen, Peter B. (1979). Seifert fibered spaces in 3-manifolds . Providence: American Mathematical Society. ISBN 0-8218-2220-9 .
Shalen, Peter B. Separating, incompressible surfaces in 3-manifolds. Inventiones Mathematicae 52 (1979), no. 2, 105–126.
Culler, Marc; Shalen, Peter B. Varieties of group representations and splittings of 3-manifolds. Annals of Mathematics (2 ) 117 (1983), no. 1, 109–146.
Culler, Marc; Gordon, C. McA.; Luecke, J.; Shalen, Peter B. Dehn surgery on knots. Annals of Mathematics (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. Annals of Mathematics (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. Annals of Mathematics (2 ) 127 (1988), no. 3, 457–519.
References
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^ Curriculum Vitæ of Peter B. Shalen Retrieved 9 November 2010
^ Sloan Research Fellowships [permanent dead link ]
^ Shalen, P. B. (1986). "Representations of 3-manifold groups and applications in topology". Proceedings of the International Congress of Mathematicians, August 3–11, 1986, Berkeley, California . Vol. 1. pp. 607–614.
^ 2017 Class of the Fellows of the AMS , American Mathematical Society , retrieved 2016-11-06.
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R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Peter_Shalen&oldid=1217697009 "
C a t e g o r i e s :
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● 2 1 s t - c e n t u r y A m e r i c a n m a t h e m a t i c i a n s
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● H a r v a r d C o l l e g e a l u m n i
● C o l u m b i a U n i v e r s i t y f a c u l t y
● R i c e U n i v e r s i t y f a c u l t y
● U n i v e r s i t y o f I l l i n o i s C h i c a g o f a c u l t y
● L i v i n g p e o p l e
● C o u r a n t I n s t i t u t e o f M a t h e m a t i c a l S c i e n c e s f a c u l t y
● F e l l o w s o f t h e A m e r i c a n M a t h e m a t i c a l S o c i e t y
● M a t h e m a t i c i a n s f r o m N e w Y o r k ( s t a t e )
● A m e r i c a n m a t h e m a t i c i a n s t u b s
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● A r t i c l e s w i t h d e a d e x t e r n a l l i n k s f r o m M a r c h 2 0 1 8
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● A r t i c l e s w i t h G N D i d e n t i f i e r s
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● A r t i c l e s w i t h L C C N i d e n t i f i e r s
● A r t i c l e s w i t h N T A i d e n t i f i e r s
● A r t i c l e s w i t h M A T H S N i d e n t i f i e r s
● A r t i c l e s w i t h M G P i d e n t i f i e r s
● A r t i c l e s w i t h Z B M A T H i d e n t i f i e r s
● A r t i c l e s w i t h S U D O C i d e n t i f i e r s
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● A b o u t W i k i p e d i a
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● M o b i l e v i e w