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William Floyd (mathematician)

October 20, 2023

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]

Dr. Floyd discusses languages over the integer lattice.

Mathematical contributions Edit

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]

References Edit

  1. ^ William J. Floyd. Mathematics Genealogy Project. Accessed February 6, 2010
  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, ISBN 0-8218-2822-3 MR1921706; pp. 63–64

External links Edit


    

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October 20, 2023
william, floyd, mathematician, william, floyd, american, mathematician, specializing, topology, currently, professor, virginia, polytechnic, institute, state, university, floyd, received, mathematics, from, princeton, university, 1978, under, direction, willia. 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 Dr Floyd discusses languages over the integer lattice Mathematical contributions EditMost 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 References Edit 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 Academiae Scientiarium Fennicae 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 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 MR1921706 pp 63 64External links EditWilliam Floyd at the Mathematics Genealogy Project William Floyd s webpage Department of Mathematics Virginia Polytechnic Institute and State University nbsp nbsp nbsp This article about an American mathematician is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title William Floyd mathematician amp oldid 1155075755, wikipedia, wiki, book, books, library,

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