John Edwin Luecke

John Edwin Luecke (born before 1960) is an American mathematician who studies the geometric topology of 3-manifolds and knot theory. He is a professor at the University of Texas at Austin .

Luecke received his PhD in 1985 from Cameron Gordon at the University of Texas at Austin (Finite covers of Haken 3-manifolds).

In 1989 he and Cameron Gordon proved that knots are determined by their complement . In 1987 he demonstrated the Cyclic Surgery Theorem with Gordon, Marc Culler and Peter Shalen . It is a theorem about the 3-manifolds with a cyclic fundamental group resulting from a stretching surgery on nodes .

Let M be a compact, connected, orientable, irreducible 3-manifold, the boundary a torus, with the closed 3-manifold M (r) with parameter r (slope) corresponding to stretching surgery . If M is not a Seifert fiber space and if the fundamental groups and for two slopes r, s are cyclic, then the minimum geometric number of intersections is so that there are a maximum of three slopes for which is cyclic. ${\displaystyle \partial M}$ ${\displaystyle \pi _{1}(M(r))}$ ${\displaystyle \pi _{1}(M(s))}$ ${\displaystyle \Delta (r,s)\leq 1}$ ${\displaystyle \pi _{1}(M(s))}$

In 1992 he received a Presidential Young Investigator Award from the NSF and in 1994 he was a Sloan Research Fellow . In 2012 he became a Fellow of the American Mathematical Society . In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich ( Dehn surgery on knots ).

Fonts (selection)

In addition to the works cited in the footnotes:

• Finite covers of 3-manifolds containing essential tori. In: Transactions of the American Mathematical Society . Volume 310, No. 1, 1988, pp. 381-391, doi : 10.2307 / 2001129 .
• with Cameron McA. Gordon: Dehn surgeries on knots creating essential tori, I. In: Communications in Analysis and Geometry. Volume 3, No. 4, 1995, pp. 597-644, doi : 10.4310 / CAG.1995.v3.n4.a3 .
• with Cameron McA. Gordon: Dehn surgeries on knots creating essential tori, II. In: Communications in Analysis and Geometry. Volume 8, No. 4, 2000, pp. 671-725, doi : 10.4310 / CAG.2000.v8.n4.a1 .
• with Cameron McA. Gordon: Reducible manifolds and Dehn surgery. In: Topology. Volume 35, No. 2, 1996, pp. 385-409, doi : 10.1016 / 0040-9383 (95) 00016-X .
• with Kenneth L. Baker and Cameron Gordon: Obtaining genus 2 Heegaard splittings from Dehn surgery. In: Algebraic & Geometric Topology . Volume 13, No. 5, 2013, pp. 2471-2634, doi : 10.2140 / agt.2013.13.2471 .
• with Kenneth L. Baker and Cameron Gordon: Bridge number, Heegaard genus and non-integral Dehn surgery. In: Transactions of the American Mathematical Society. Volume 367, 2015, pp. 5753-5830, doi : 10.1090 / S0002-9947-2014-06328-9 .
• with Kenneth L. Baker and Cameron Gordon: Bridge number and integral Dehn surgery. In: Algebraic & Geometric Topology. Volume 16, No. 1, 2016, pp. 1-40, doi : 10.2140 / agt.2016.16.1 .

Web links

• University of Texas website

Individual evidence

1. ↑ John Edwin Luecke in the Mathematics Genealogy Project (English)
2. ↑ Cameron McA. Gordon, John Luecke: Knots are determined by their complements. In: Journal American Mathematical Society. Vol. 2, No. 2, 1989, pp. 371-415, ( digitized version ).
3. ↑ Marc Culler, Cameron McA. Gordon, John Luecke, Peter B. Shalen: Dehn surgery on knots. In: Annals of Mathematics . Vol. 125, No. 2, 1987, pp. 237-300, doi : 10.2307 / 1971311 ; Correction, Volume 127, No. 3, 1988, p. 663, doi : 10.2307 / 2007009 .