John Edwin Luecke
Encyclopedia
John Edwin Luecke is an American mathematician who works in topology
and knot theory
. He got his Ph.D. in 1985 from the University of Texas at Austin
and is now a professor in the department of mathematics at that institution.
s. In a 1987 paper Luecke, Marc Culler
, Cameron Gordon
, and Peter Shalen
proved the cyclic surgery theorem
. In a 1989 paper Luecke and Cameron Gordon proved that knots are determined by their complements, a result now known as the Gordon–Luecke theorem.
Dr Luecke received a NSF
Presidential Young Investigator Award
in 1992 and Sloan Foundation fellow in 1994.
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
. He got his Ph.D. in 1985 from the University of Texas at Austin
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
and is now a professor in the department of mathematics at that institution.
Work
Luecke specializes in knot theory and 3-manifold3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
s. In a 1987 paper Luecke, Marc Culler
Marc Culler
Marc Edward Culler 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...
, Cameron Gordon
Cameron Gordon (mathematician)
Cameron Gordon is a Professor and Sid W. Richardson Foundation Regents Chair in the Department 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...
, and 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, and went on to earn a B.A. from Harvard College in 1966 and his Ph.D. from Harvard University in 1972...
proved the cyclic surgery theorem
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 on T such that their Dehn fillings have cyclic...
. In a 1989 paper Luecke and Cameron Gordon proved that knots are determined by their complements, a result now known as the Gordon–Luecke theorem.
Dr Luecke received a NSF
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
Presidential Young Investigator Award
Presidential Young Investigator Award
The Presidential Young Investigator Award was awarded by the National Science Foundation. The program operated from 1984 to 1991, and was replaced by the NSF Young Investigator Awards and Presidential Faculty Fellows Program...
in 1992 and Sloan Foundation fellow in 1994.