Biography: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]
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 [math]\displaystyle{ \mathbb{R}^4 }[/math] with four critical points are standard" Inventiones mathematicae, 1985
- "Tunnel number one knots satisfy the Poenaru conjecture" Topology and its Applications, 1984
- with A Thompson – "Detecting unknotted graphs in 3-space" Journal of Differential Geometry, 1991
- with A Thompson – "Thin position and Heegaard splittings of the 3-sphere" J. Differential Geom, 1994
References
- ↑ "Curriculum Vitae – Martin Scharlemann". http://www.math.ucsb.edu/~mgscharl/concise.html.
- ↑ 2.0 2.1 "The Mathematics Genealogy Project – Martin Scharlemann". http://www.genealogy.math.ndsu.nodak.edu/id.php?id=16934.
- ↑ "Geometric Topology in Dimensions 3 and 4". http://users.math.yale.edu/~jj327/conference/.
- ↑ https://www.ams.org/profession/ams-fellows/fellows2014.pdf [bare URL PDF]
- ↑ "Detecting unknotted graphs in 3-space" (in en). Journal of Differential Geometry 34 (2): 539–560. 1991. doi:10.4310/jdg/1214447220.
- ↑ Lackenby, Marc (1997-08-01). "Surfaces, surgery and unknotting operations" (in en). Mathematische Annalen 308 (4): 615–632. doi:10.1007/s002080050093. ISSN 0025-5831.
- ↑ 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.
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