William Floyd (mathematician)
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.
In a 1980 paper Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary. Floyd also wrote a number of joint papers with J. W. Cannon and W. R. Parry exploring a combinatorial approach to the Cannon conjecture using finite subdivision rules. This represents one of the few plausible lines of attack of the conjecture.
- William J. Floyd. Mathematics Genealogy Project. Accessed February 6, 2010
- Floyd, W.; Hatcher, A. Incompressible surfaces in punctured-torus bundles. Topology and its Applications, vol. 13 (1982), no. 3, pp. 263–282
- Floyd, William J., Group completions and limit sets of Kleinian groups. Inventiones Mathematicae, vol. 57 (1980), no. 3, pp. 205–218
- 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
- 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.
- 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
- William Floyd's webpage, Department of Mathematics, Virginia Polytechnic Institute and State University
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