William Floyd (mathematician) explained

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.^[1]

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.^[2]

In a 1980 paper^[3] Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary.^{[4] [5]} Floyd also wrote a number of joint papers with James W. Cannon and Walter R. Parry exploring a combinatorial approach to the Cannon conjecture^{[6] [7] [8]} using finite subdivision rules. This represents one of the few plausible lines of attack of the conjecture.^[9]

External links

• • William Floyd's webpage, Department of Mathematics, Virginia Polytechnic Institute and State University

Notes and References

1. http://genealogy.math.ndsu.nodak.edu/id.php?id=7658 William J. Floyd.
2. Floyd, W.; Hatcher, A.Incompressible surfaces in punctured-torus bundles. Topology and its Applications, vol. 13 (1982), no. 3, pp. 263 - 282
3. Floyd, William J., Group completions and limit sets of Kleinian groups. Inventiones Mathematicae, vol. 57 (1980), no. 3, pp. 205 - 218
4. Karlsson, Anders, Free subgroups of groups with nontrivial Floyd boundary. Communications in Algebra, vol. 31 (2003), no. 11, pp. 5361 - 5376.
5. 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
6. 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.
7. J. W. Cannon, W. J. Floyd, W. R. Parry. Finite subdivision rules. Conformal Geometry and Dynamics, vol. 5 (2001), pp. 153 - 196.
8. 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.
9. 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, ; pp. 63 - 64