William Floyd (mathematician)

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 paperFloyd, 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 James W. Cannon and Walter R. Parry exploring a combinatorial approach to the Cannon conjectureJ. 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.Ilya Kapovich, and Nadia Benakli, in Boundaries of hyperbolic groups, Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 39–93, Contemporary Mathematics, 296, American Mathematical Society, Providence, RI, 2002, {{isbn|0-8218-2822-3}} {{MR|1921706}}; pp. 63–64

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• {{MathGenealogy|7658}}
• [http://www.math.vt.edu/people/floyd/ William Floyd's webpage], Department of Mathematics, Virginia Polytechnic Institute and State University

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