Martin Scharlemann

Martin George Scharlemann is an American topologist who is a professor at University of California, Santa Barbara.[1] He obtained his Ph.D. under the guidance of Robion Kirby in 1974.[2]

A conference is his honor was held in 2009 at University of California, Davis.[3] He is a Fellow of the American Mathematical Society, for his "contributions to low-dimensional topology and knot theory."[4]

Abigail Thompson was a student of his.[2] Together they solved the graph planarity problem: There is an algorithm to decide whether a finite graph in 3-space can be moved in 3-space into a plane.[5]

He gave the first proof of the classical theorem that knots with unknotting number one are prime. He used hard combinatorial arguments for this. Simpler proofs are now known.[6][7]

Selected publications

  • "Producing reducible 3-manifolds by surgery on a knot" Topology, 1990
  • with A Thompson – "Heegaard splittings of (surface) x I are standard" Mathematische Annalen, 1993
  • "Sutured manifolds and generalized Thurston norms" J. Diff. Geom., 1989
  • with H Rubinstein – "Comparing Heegaard splittings of non-Haken 3-manifolds" Topology, 1996
  • "Unknotting number one knots are prime" Inventiones mathematicae, 1985
  • with M Tomova – "Alternate Heegaard genus bounds distance" Geometry & Topology, 2006

References

  1. ↑ "Curriculum Vitae – Martin Scharlemann".
  2. 1 2 "The Mathematics Genealogy Project – Martin Scharlemann".
  3. ↑ "Geometric Topology in Dimensions 3 and 4".
  4. ↑ http://www.ams.org/profession/ams-fellows/fellows2014.pdf
  5. ↑ Scharlemann, Martin; Thompson, Abigail (1991). "Detecting unknotted graphs in 3-space". Journal of Differential Geometry. 34: 539–560.
  6. ↑ Lackenby, Marc (1997-08-01). "Surfaces, surgery and unknotting operations". Mathematische Annalen. 308 (4): 615–632. doi:10.1007/s002080050093. ISSN 0025-5831.
  7. ↑ Zhang, Xingru (1991-01-01). "Unknotting Number One Knots are Prime: A New Proof". Proceedings of the American Mathematical Society. 113 (2): 611–612. doi:10.2307/2048550. JSTOR 2048550.
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