Martin Scharlemann Explained
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. Together they solved the graph planarity problem: There isan 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 29 (1990), no. 4, 481–500.
- with Abigail Thompson, "Heegaard splittings of (surface) x I are standard" Mathematische Annalen 295 (1993), no. 3, 549–564.
- "Sutured manifolds and generalized Thurston norms", Journal of Differential Geometry 29 (1989), no. 3, 557–614.
- with J. Hyam Rubinstein, "Comparing Heegaard splittings of non-Haken 3-manifolds" Topology 35 (1996), no. 4, 1005–1026
- "Unknotting number one knots are prime", Inventiones mathematicae 82 (1985), no. 1, 37–55.
- with Maggy Tomova, "Alternate Heegaard genus bounds distance" Geometry & Topology 10 (2006), 593–617.
- "Local detection of strongly irreducible Heegaard splittings" Topology and its Applications, 1998
- with Abigail Thompson – "Link genus and the Conway moves" Commentarii Mathematici Helvetici, 1989
- "Smooth spheres in
with four critical points are standard"
Inventiones mathematicae, 1985
Notes and References
- Web site: Curriculum Vitae – Martin Scharlemann.
- Web site: The Mathematics Genealogy Project – Martin Scharlemann.
- Web site: Geometric Topology in Dimensions 3 and 4.
- 2014 Class of the Fellows of the AMS. Notices of the American Mathematical Society. 61. 4. 420–421. April 2014.
- Scharlemann. Martin. Thompson. Abigail. 1991. Detecting unknotted graphs in 3-space. Journal of Differential Geometry. en. 34. 2. 539–560. 10.4310/jdg/1214447220. free.
- Lackenby. Marc. 1997-08-01. Surfaces, surgery and unknotting operations. Mathematische Annalen. en. 308. 4. 615–632. 10.1007/s002080050093. 121512073. 0025-5831.
- Zhang. Xingru. 1991-01-01. Unknotting Number One Knots are Prime: A New Proof. 2048550. Proceedings of the American Mathematical Society. 113. 2. 611–612. 10.2307/2048550. free.