Martin Scharlemann

{{short description|American mathematician}}

Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara.{{cite web|url=http://www.math.ucsb.edu/~mgscharl/concise.html|title=Curriculum Vitae – Martin Scharlemann|publisher=}} He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974.{{cite web|url=http://www.genealogy.math.ndsu.nodak.edu/id.php?id=16934|title=The Mathematics Genealogy Project – Martin Scharlemann|publisher=}}

A conference in his honor was held in 2009 at the University of California, Davis.{{cite web|url=http://users.math.yale.edu/~jj327/conference/|title=Geometric Topology in Dimensions 3 and 4|publisher=}} He is a Fellow of the American Mathematical Society, for his "contributions to low-dimensional topology and knot theory."{{cite journal|url=https://www.ams.org/profession/ams-fellows/fellows2014.pdf|journal=Notices of the American Mathematical Society|title=2014 Class of the Fellows of the AMS|volume=61|issue=4|pages=420–421|date=April 2014}}

Abigail Thompson was a student of his. 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.{{Cite journal|author1-last=Scharlemann|author1-first=Martin|author2-last=Thompson|author2-first=Abigail|year=1991|title=Detecting unknotted graphs in 3-space|journal=Journal of Differential Geometry|language=en|volume=34|issue=2|pages=539–560|doi=10.4310/jdg/1214447220|doi-access=free}}

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.{{Cite journal|last=Lackenby|first=Marc|date=1997-08-01|title=Surfaces, surgery and unknotting operations|journal=Mathematische Annalen|language=en|volume=308|issue=4|pages=615–632|doi=10.1007/s002080050093|s2cid=121512073|issn=0025-5831}}{{Cite journal|last=Zhang|first=Xingru|date=1991-01-01|title=Unknotting Number One Knots are Prime: A New Proof|jstor=2048550|journal=Proceedings of the American Mathematical Society|volume=113|issue=2|pages=611–612|doi=10.2307/2048550|doi-access=free}}