William Floyd - Research

Research

Preprints
- Constructing subdivision rules from rational maps
  Abstract, PostScript file (346 Kb) , pdf file (135 Kb)
- William Floyd, Leslie Kay, and Michael Shapiro
  Some elementary properties of SIR networks
  pdf file (148 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Expansion complexes for finite subdivisiion rules I
  Abstract, gzipped PostScript file (479 Kb) , pdf file (526 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Expansion complexes for finite subdivisiion rules II
  Abstract, gzipped PostScript file (1,310 Kb) , pdf file (1,113 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Combinatorially regular polyomino tilings
  Abstract, gzipped PostScript file (544 Kb) , pdf file (271 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  A survey of twisted face-pairing 3-manifolds
  Abstract, gzipped PostScript file (1,011 Kb) , pdf file (338 Kb)
- W. Floyd, B. Weber, and J. Weeks
  The Achilles' heel of O(3,1)?
  Abstract, gzipped PostScript file (1,128 Kb), pdf file (322 Kb)
- J. W. Cannon, W. J. Floyd, R. Kenyon, and W. R. Parry
  Constructing rational maps from subdivision rules
  Abstract, compressed PostScript file (1,932 Kb) , pdf file (1,329 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds
  Abstract, compressed PostScript file (2,240 Kb) , pdf file (503 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Ample twisted face-pairing 3-manifolds
  - gzipped Postcript file (5762 Kb) (The postscript file contains one 18 MByte figure.)
  - The same paper, but without three of the circlepacking figures.
    gzipped Postscript file (1251 Kb), pdf file (882 Kb),
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Introduction to twisted face-pairings
  pdf file (301 KB), gzipped Postcript file (312 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Finite subdivision rules
  Abstract, compressed PostScript file (2,345 Kb), pdf file (1,444 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Sufficiently Rich Families of Planar Rings
  Abstract, compressed PostScript file (1,100 Kb), pdf file (1,332 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Conformal modulus: the graph paper invariant or The conformal shape of an algorithm
  Abstract, compressed PostScript file (1,270 Kb), pdf file (336 Kb)
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  The length-area method and discrete Riemann mappings
  pdf file (1,270 Kb), gzipped Postcript file (1,915 Kb)
- E. E. Floyd and W. J. Floyd
  Actions of Classical Small Categories
  Abstract, compressed PostScript file (1,745 Kb), pdf file (2,317 Kb)
Selected Reprints
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Twisted face-pairing 3-manifolds, Trans. Amer. Math. Soc. 354 (2002), 2369-2397.
- J. W. Cannon, W. J. Floyd, and W. R. Parry
  Finite subdivision rules, Conform. Geom. Dyn. 5 (2001), 153-196.
- J. W. Cannon, W. J. Floyd, R. Kenyon, and W. R. Parry
  Hyperbolic Geometry, in Flavors of Geometry, edited by Silvio Levy, MSRI Publication Number 31, 1997.
Electronic talks
- Cannon's conjecture, finite subdivision rules, and rational maps Groups 2007, Luminy, 19 February 2007
- A critically finite map, and the associated map on Teichmueller space Spring Topology and Dynamics Conference 2007, Rolla, 31 March 2007
- Finite subdivision rulesCircle Packing, Minimal Surfaces, and Discrete Differential Geometry, ICERM, 13 February 2025
Software - written by J. W. Cannon, W. J. Floyd, and W. R. Parry
- Subdivision programs
- Twisted face pairing 3-manifolds
  - pairsnap.c (formerly tilesnap.c)
  - partsnap.c (formerly twisttor.c)
  - cellsnap.c
  - bitwist.c

This site contains work supported by National Science Foundation grants DMS-9971783, DMS-9803868, DMS-10104030, and DMS-0203902. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).