Martin Scharlemann

Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara.[1] He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974.[2]

A conference in his honor was held in 2009 at the 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]

  1. ^ "Curriculum Vitae – Martin Scharlemann".
  2. ^ a b "The Mathematics Genealogy Project – Martin Scharlemann".
  3. ^ "Geometric Topology in Dimensions 3 and 4".
  4. ^ "2014 Class of the Fellows of the AMS" (PDF). Notices of the American Mathematical Society. 61 (4): 420–421. April 2014.
  5. ^ Scharlemann, Martin; Thompson, Abigail (1991). "Detecting unknotted graphs in 3-space". Journal of Differential Geometry. 34 (2): 539–560. doi:10.4310/jdg/1214447220.
  6. ^ Lackenby, Marc (1997-08-01). "Surfaces, surgery and unknotting operations". Mathematische Annalen. 308 (4): 615–632. doi:10.1007/s002080050093. ISSN 0025-5831. S2CID 121512073.
  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.