Martin John Dunwoody (born 3 November 1938) is an emeritus professor of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the

University of Southampton , mottoeng = The Heights Yield to Endeavour , type = Public research university , established = 1862 – Hartley Institution1902 – Hartley University College1913 – Southampton University Coll ...

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...

. He earned his PhD in 1964 from the

Australian National University The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...

. He held positions at the

University of Sussex , mottoeng = Be Still and Know , established = , type = Public research university , endowment = £14.4 million (2020) , budget = £319.6 million (2019–20) , chancellor = Sanjeev Bhaskar , vice_chancellor = Sasha Roseneil , ...

before becoming a professor at the

in 1992. He has been emeritus professor since 2003. Dunwoody works on

geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such group (mathematics), groups and topology, topological and geometry, geometric pro ...

and

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

. He is a leading expert in splittings and accessibility of discrete groups, groups acting on graphs and trees, JSJ-decompositions, the topology of 3-manifolds and the structure of their

fundamental group In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...

s. Since 1971 several mathematicians have been working on Wall's conjecture, posed by Wall in a 1971 paper, which said that all finitely generated groups are accessible. Roughly, this means that every finitely generated group can be constructed from finite and one-ended groups via a finite number of amalgamated free products and

HNN extension In mathematics, the HNN extension is an important construction of combinatorial group theory. Introduced in a 1949 paper ''Embedding Theorems for Groups'' by Graham Higman, Bernhard Neumann, and Hanna Neumann, it embeds a given group ''G'' into an ...

s over finite subgroups. In view of the

Stallings theorem about ends of groups In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group ''G'' has more than one end if and only if the group ''G'' admits a nontrivial decomposition as an amalgamated free produ ...

, 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 In mathematics, a presentation is one method of specifying a group. A presentation of a group ''G'' comprises a set ''S'' of generators—so that every element of the group can be written as a product of powers of some of these generators—and ...

s in 1985. In 1991 he finally disproved Wall's conjecture by finding a

finitely generated group In algebra, a finitely generated group is a group ''G'' that has some finite generating set ''S'' so that every element of ''G'' can be written as the combination (under the group operation) of finitely many elements of ''S'' and of inverses o ...

that is not accessible. Dunwoody found a graph-theoretic proof of 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 In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured ...

. The proof generated considerable interest among mathematicians, but a mistake was quickly discovered and the proof was withdrawn. George G. Szpiro
The secret life of numbers: 50 easy pieces on how mathematicians work and think.
National Academies Press, 2006. ; p. 19 The conjecture was later proven by

Grigori Perelman Grigori Yakovlevich Perelman ( rus, links=no, Григорий Яковлевич Перельман, p=ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman, a=Ru-Grigori Yakovlevich Perelman.oga; born 13 June 1966) is a Russian mathemati ...

, following the program of Richard S. Hamilton.

References

External links

home page
of Martin Dunwoody. * {{DEFAULTSORT:Dunwoody, Martin 1938 births Living people 20th-century British mathematicians 21st-century British mathematicians Australian National University alumni Academics of the University of Sussex Academics of the University of Southampton