Editing Martin Dunwoody

{{Short description|British mathematician}}
{{Use dmy dates|date=June 2020}}
{{Use British English|date=December 2011}}
'''Martin John Dunwoody''' (born 3 November 1938) is an emeritus professor of [[Mathematics]] at the [[University of Southampton]], [[England]].

He earned his PhD in 1964 from the [[Australian National University]]. He held positions at the [[University of Sussex]] before becoming a professor at the [[University of Southampton]] in 1992. He has been emeritus professor since 2003.<ref>{{Cite web|url=https://www.southampton.ac.uk/maths/about/staff/mjd7.page|title=Professor Martin Dunwoody {{!}} Mathematical Sciences {{!}} University of Southampton|website=www.southampton.ac.uk|access-date=2019-06-17}}</ref>

Dunwoody works on [[geometric group theory]] and [[low-dimensional topology]]. He is a leading expert in [[Stallings theorem about ends of groups|splittings and accessibility of discrete groups]], groups acting on graphs and trees, [[Bass–Serre theory|JSJ-decompositions]], the topology of [[3-manifold]]s and the structure of their [[fundamental group]]s.

Since 1971 several mathematicians have been working on [[C. T. C. Wall|Wall's conjecture]], posed by Wall in a 1971 paper,<ref>[[C. T. C. Wall|Wall, C. T. C.]],
''Pairs of relative cohomological dimension one.''
[[Journal of Pure and Applied Algebra]], vol. 1 (1971), no. 2, pp. 141&ndash;154</ref> which said that all finitely generated groups are accessible. Roughly, this means that every finitely generated group can be constructed from finite and [[Stallings theorem about ends of groups|one-ended]] groups via a finite number of [[free product|amalgamated free products]] and [[HNN extension]]s over finite subgroups. In view of the [[Stallings theorem about ends of groups]], one-ended groups are precisely those finitely generated infinite groups that cannot be decomposed nontrivially as amalgamated products or HNN-extensions over finite subgroups.
Dunwoody proved the Wall conjecture for [[finitely presented group]]s in 1985.<ref>Dunwoody, M. J., ''The accessibility of finitely presented groups.''
[[Inventiones Mathematicae]], vol. 81 (1985), no. 3, pp. 449&ndash;45</ref> In 1991 he finally disproved Wall's conjecture by finding a [[finitely generated group]] that is not accessible.<ref>Dunwoody, Martin J. ''An inaccessible group''. Geometric group theory, Vol. 1 (Sussex, 1991), pp. 75&ndash;78, London Math. Soc. Lecture Note Ser., 181, [[Cambridge University Press]], Cambridge, 1993. {{ISBN|0-521-43529-3}}</ref>

Dunwoody found a graph-theoretic proof of [[Stallings theorem about ends of groups|Stallings' theorem about ends of groups]] in 1982, by constructing certain tree-like automorphism invariant graph decompositions. This work has been developed to an important theory in the book ''Groups acting on graphs'', Cambridge University Press, 1989, with Warren Dicks. In 2002 Dunwoody put forward a proposed proof of the [[Poincaré conjecture]].<ref>[https://web.archive.org/web/20110605031440/http://www.telegraph.co.uk/science/science-news/3293446/British-professor-chases-solution-to-1m-maths-prize.html British professor chases solution to $1m maths prize.] [[Daily Telegraph]], 14 April 2002. Accessed 23 January. 2010</ref> The proof generated considerable interest among mathematicians, but a mistake was quickly discovered and the proof was withdrawn.<ref>[[George Szpiro|George G. Szpiro]], [https://books.google.com/books?id=qIXl0kEwrVMC&pg=PA51 The secret life of numbers: 50 easy pieces on how mathematicians work and think.]  National Academies Press, 2006. {{ISBN|0-309-09658-8}}; p. 19</ref> The conjecture was later proven by [[Grigori Perelman]], following the program of [[Richard S. Hamilton]].

==References==
{{reflist}}

== External links ==
* [http://www.personal.soton.ac.uk/mjd7/ home page] of Martin Dunwoody.
* {{MathGenealogy|id=57371}}

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[[Category:1938 births]]
[[Category:Living people]]
[[Category:20th-century British mathematicians]]
[[Category:21st-century British mathematicians]]
[[Category:Australian National University alumni]]
[[Category:Academics of the University of Sussex]]
[[Category:Academics of the University of Southampton]]