Cameron Gordon

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Cameron McAllan Gordon (* 1945 ) is a British mathematician who studies geometric topology (including knot theory ). He is a professor at the University of Texas at Austin .

Cameron Gordon 2010

Gordon received his PhD in 1971 from the University of Cambridge with John FP Hudson ( Knots and Embeddings ).

In 1987 he proved the Cyclic Surgery Theorem with Marc Culler , John Edwin Luecke and Peter Shalen . Building on this, he and his doctoral student Luecke (1985) showed that nodes are determined by their complement ( theorem of Gordon-Luecke ): every homeomorphism between two node complements in the 3-sphere can be turned into a homeomorphism of the 3-sphere expand.

He was involved in the solution of the Smith Conjecture (drawn up by Paul A. Smith ). With Andrew Casson he introduced the Casson-Gordon invariants into knot theory and proved fundamental theorems about highly irreducible Heegaard decompositions .

He was a 1999 Guggenheim Fellow , he was a Sloan Fellow and is a Fellow of the Royal Society of Edinburgh .

Fonts

  • Editor with Robion Kirby Four-Manifold Theory , American Mathematical Society 1984
  • Editor with Yoav Moriah, Bronislaw Wajnryb Geometric topology: Joint US-Israel Workshop on Geometric Topology, June 10-16, 1992, Technion, Haifa, Israel , American Mathematical Society 1994
  • with Ying-Qing Wu: Toroidal Dehn fillings on hyperbolic 3-manifolds , American Mathematical Society 2008
  • with John Luecke: Non-integral toroidal Dehn surgeries. Comm. Anal. Geom. 12 (2004), no. 1-2, 417-485.
  • Boundary slopes of punctured tori in 3 -manifolds. Trans. Amer. Math. Soc. 350 (1998) no. 5, 1713-1790.
  • with John Luecke: Reducible manifolds and Dehn surgery. Topology 35 (1996) no. 2, 385-409.
  • Dehn surgery on knots. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 631-642, Math. Soc. Japan, Tokyo, 1991.
  • with John Luecke: Knots are determined by their complements. J. Amer. Math. Soc. 2 (1989) no. 2, 371-415.
  • with Andrew Casson: Reducing Heegaard splittings. Topology Appl. 1987, 27, no. 3, 275-283.
  • with Marc Culler, John Luecke, Peter Shalen: Dehn surgery on knots. Ann. of Math. (2) 125 (1987) no. 2, 237-300.
  • with Andrew Casson: Cobordism of classical knots , in A. Marin, L. Guillou A la recherche de la topologie perdue , Progress in Mathematics, Birkhäuser 1986
  • with Rick Litherland: Incompressible planar surfaces in 3 -manifolds. Topology Appl. 18 (1984) no. 2-3, 121-144.
  • with John Conway: Knots and links in spatial graphs. J. Graph Theory 7 (1983), no. 4, 445-453.
  • with Andrew Casson On slice knots in dimension three , Proc. Symp. Pure Math., Volume 32, American Mathematical Society 1978
  • with Rick Litherland: On the signature of a link. Invent. Math. 47 (1978) no. 1, 53-69.

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Culler, Gordon, Luecke, Shalen Dehn surgery on knots , Annals of Mathematics, Volume 125, 1987, pp. 237-300
  3. ↑ Gordon, Luecke Knots are determined by their complements , J. Amer. Math. Soc., Vol. 2, 1989, pp. 371-415
  4. ^ Casson, Gordon Reducing Heegaard splittings , Topology and its Applications, Volume 27, 1987, pp. 275-283
personal data
SURNAME Gordon, Cameron
ALTERNATIVE NAMES Gordon, Cameron McAllen
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH 1945