Since 1971 several mathematicians have been working on Wall's conjecture, posed by Wall in a 1971 paper,[2] 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 extensions 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 groups in 1985.[3] In 1991 he finally disproved Wall's conjecture by finding a finitely generated group that is not accessible.[4]
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.[5] The proof generated considerable interest among mathematicians, but a mistake was quickly discovered and the proof was withdrawn.[6] The conjecture was later proven by Grigori Perelman, following the program of Richard S. Hamilton.
Referencesedit
^"Professor Martin Dunwoody | Mathematical Sciences | University of Southampton". www.southampton.ac.uk. Retrieved 17 June 2019.
^Dunwoody, M. J., The accessibility of finitely presented groups.Inventiones Mathematicae, vol. 81 (1985), no. 3, pp. 449–45
^Dunwoody, Martin J. An inaccessible group. Geometric group theory, Vol. 1 (Sussex, 1991), pp. 75–78, London Math. Soc. Lecture Note Ser., 181, Cambridge University Press, Cambridge, 1993. ISBN0-521-43529-3
^George G. Szpiro, The secret life of numbers: 50 easy pieces on how mathematicians work and think. National Academies Press, 2006. ISBN0-309-09658-8; p. 19
martin, dunwoody, martin, john, dunwoody, born, november, 1938, emeritus, professor, mathematics, university, southampton, england, earned, 1964, from, australian, national, university, held, positions, university, sussex, before, becoming, professor, universi. 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 1 Dunwoody works on geometric group theory and low dimensional topology 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 groups Since 1971 several mathematicians have been working on Wall s conjecture posed by Wall in a 1971 paper 2 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 extensions 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 groups in 1985 3 In 1991 he finally disproved Wall s conjecture by finding a finitely generated group that is not accessible 4 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 Poincare conjecture 5 The proof generated considerable interest among mathematicians but a mistake was quickly discovered and the proof was withdrawn 6 The conjecture was later proven by Grigori Perelman following the program of Richard S Hamilton References edit Professor Martin Dunwoody Mathematical Sciences University of Southampton www southampton ac uk Retrieved 17 June 2019 Wall C T C Pairs of relative cohomological dimension one Journal of Pure and Applied Algebra vol 1 1971 no 2 pp 141 154 Dunwoody M J The accessibility of finitely presented groups Inventiones Mathematicae vol 81 1985 no 3 pp 449 45 Dunwoody Martin J An inaccessible group Geometric group theory Vol 1 Sussex 1991 pp 75 78 London Math Soc Lecture Note Ser 181 Cambridge University Press Cambridge 1993 ISBN 0 521 43529 3 British professor chases solution to 1m maths prize Daily Telegraph 14 April 2002 Accessed 23 January 2010 George G Szpiro The secret life of numbers 50 easy pieces on how mathematicians work and think National Academies Press 2006 ISBN 0 309 09658 8 p 19External links edithome page of Martin Dunwoody Martin Dunwoody at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Martin Dunwoody amp oldid 1034977409, wikipedia, wiki, book, books, library,
