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William J. Floyd is an American mathematician specializing in topology. He is currently a professor at Virginia Polytechnic Institute and State University. Floyd received a PhD in Mathematics from Princeton University 1978 under the direction of William Thurston.〔(William J. Floyd. ) Mathematics Genealogy Project. Accessed February 6, 2010〕 ==Mathematical contributions== Most of Floyd's research is in the areas of geometric topology and geometric group theory. Floyd and Allen Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle.〔Floyd, W.; Hatcher, A. ''Incompressible surfaces in punctured-torus bundles.'' Topology and its Applications, vol. 13 (1982), no. 3, pp. 263–282〕 In a 1980 paper〔Floyd, William J., ''Group completions and limit sets of Kleinian groups.'' Inventiones Mathematicae, vol. 57 (1980), no. 3, pp. 205–218〕 Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary.〔Karlsson, Anders, ''Free subgroups of groups with nontrivial Floyd boundary.'' Communications in Algebra, vol. 31 (2003), no. 11, pp. 5361–5376.〕〔Buckley, Stephen M.; Kokkendorff, Simon L., ''Comparing the Floyd and ideal boundaries of a metric space.'' Transactions of the American Mathematical Society, vol. 361 (2009), no. 2, pp. 715–734〕 Floyd also wrote a number of joint papers with J. W. Cannon and W. R. Parry exploring a combinatorial approach to the Cannon conjecture〔J. W. Cannon, W. J. Floyd, W. R. Parry. ''Sufficiently rich families of planar rings.'' Annales Academiæ Scientiarium Fennicæ. Mathematica. vol. 24 (1999), no. 2, pp. 265–304.〕〔J. W. Cannon, W. J. Floyd, W. R. Parry. ''Finite subdivision rules''. Conformal Geometry and Dynamics, vol. 5 (2001), pp. 153–196.〕〔J. W. Cannon, W. J. Floyd, W. R. Parry. ''Expansion complexes for finite subdivision rules. I. ''Conformal Geometry and Dynamics, vol. 10 (2006), pp. 63–99.〕 using finite subdivision rules. This represents one of the few plausible lines of attack of the conjecture.〔I. Kapovich, and N. Benakli, (''Boundaries of hyperbolic groups.'' ) Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 39–93, Contemp. Math., 296, American Mathematical Society, Providence, RI, 2002, ISBN 0-8218-2822-3; pp. 63–64〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「William Floyd (mathematician)」の詳細全文を読む スポンサード リンク
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