Marc Culler

Marc Culler
Marc Culler

Photograph by Roberta Devlin
Born November 22, 1953
Nationality American
Fields geometric group theory
low-dimensional topology
Alma mater University of California, Berkeley
Doctoral advisor John Robert Stallings
Known for cyclic surgery theorem
Culler–Vogtmann Outer space

Marc Edward Culler (born November 22, 1953) is an American mathematician who works in geometric group theory and low-dimensional topology. A native Californian, Culler did his undergraduate work at the University of California at Santa Barbara and his graduate work at Berkeley where he graduated in 1978. He is now at the University of Illinois at Chicago. Culler is the son of Glen Jacob Culler who was an important early innovator in the development of the Internet.

Contents

Work

Culler specializes in group theory,[1] low dimensional topology, 3-manifolds, and hyperbolic geometry. Culler frequently collaborates with Peter Shalen and they have co-authored many papers.[2][3] Culler and Shalen did joint work that related properties of representation varieties of hyperbolic 3-manifold groups to decompositions of 3-manifolds. In particular, Culler and Shalen used the Bass–Serre theory, applied to the function field of the SL(2,C)-Character variety of a 3-manifold, to obtain information about incompressible surfaces in the manifold. Based on this work, Shalen, Cameron Gordon, John Luecke, and Culler proved the cyclic surgery theorem.

Another important contribution by Culler came in a 1986 paper with Karen Vogtmann called "Moduli of graphs and automorphisms of free groups".[4] This paper introduced an object that came to be known as Culler–Vogtmann Outer space.

Culler is one of the authors of a 1994 paper called "Plane curves associated to character varieties of 3-manifolds"[5] which introduced the A-polynomial of a knot[6] or, more generally, of a 3-manifold with one torus boundary component.

Culler is an editor of The New York Journal of Mathematics.[7] He was a Sloan Foundation Research Fellow[8] (1986–1988) and a UIC University Scholar[9][10] (2008).

Selected publications

  • 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.
  • Marc Culler and Karen Vogtmann; A group-theoretic criterion for property A. Proc. Amer. Math. Soc., 124(3):677—683, 1996. MR1307506

References

  1. ^ People in Geometric Group Theory
  2. ^ Culler, Marc; Shalen, Peter B. Varieties of group representations and splittings of 3-manifolds. Ann. of Math. (2) 117 (1983), no. 1, 109–146.
  3. ^ Culler, Marc; Gordon, C. McA.; Luecke, J.; Shalen, Peter B. Dehn surgery on knots. Ann. of Math. (2) 125 (1987), no. 2, 237–300
  4. ^ Culler, Marc; Vogtmann, Karen (1986), "Moduli of graphs and automorphisms of free groups", Inventiones Mathematicae 84 (1): 91–119, doi:10.1007/BF01388734, http://www.math.cornell.edu/~vogtmann/ScannedPapers/1986.0084.pdf. 
  5. ^ D. Cooper, M. Culler, H. Gillet, D. D. Long and P. B. Shalen. Plane curves associated to character varieties of 3-manifolds. Invent. Math., 118(1):47--84, 1994.
  6. ^ The A-polynomial and the FFT, in PDF format
  7. ^ New York Journal of Mathematics
  8. ^ Sloan Research Fellowships
  9. ^ UIC News: 2008 University Scholar Marc Culler
  10. ^ UIC College awards

External links


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Culler — is a surname, and may refer to: David Culler, computer scientist Dick Culler (1915 1964), baseball shortstop Glen Culler (1927 2003), professor of electrical engineering Marc Culler (born 1953), American mathematician Jonathan Culler (born 1944) …   Wikipedia

  • Peter Shalen — Peter B. Shalen is an American mathematician, working primarily in low dimensional topology. He is the S in JSJ decomposition. LifeHe graduated from Stuyvesant High School in 1962, [cite web |url=http://65.104.11.121/MathTeam.html… …   Wikipedia

  • Karen Vogtmann — (* 13. Juli 1949 in Pittsburg (Kalifornien)) ist eine US amerikanische Mathematikerin, die sich mit Algebra und Topologie beschäftigt. Vogtmann 1982 Vogtmann studierte an der University of California, Berkeley, wo sie 1971 ihren Bachelorabschluss …   Deutsch Wikipedia

  • SnapPea — is free software designed to help mathematicians, in particular low dimensional topologists, study hyperbolic 3 manifolds. The primary developer is Jeffrey Weeks, who created the first version as part of his doctoral thesis. The latest version is …   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

  • 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

  • Gordon-Luecke theorem — In mathematics, the Gordon Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… …   Wikipedia

  • Gordon–Luecke theorem — In mathematics, the Gordon–Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… …   Wikipedia

  • Jacques Derrida — Derrida redirects here. For the documentary film, see Derrida (film). For the physicist, see Bernard Derrida. Jacques Derrida Full name Jacques Derrida Born July 15, 1930(1930 07 15) El Biar ( …   Wikipedia

  • C10k problem — Le c10k problem[note 1] que l on pourrait traduire en français par le problème des dix mille connexions simultanées, est un code numérique utilisé pour exprimer la limitation que la plupart des serveurs ont en termes de connexions réseaux. Cette… …   Wikipédia en Français

Share the article and excerpts

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