William J. Floyd is an American mathematician specializing in

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. He is currently a professor at

Virginia Polytechnic Institute and State University The Virginia Polytechnic Institute and State University, commonly referred to as Virginia Tech (VT), is a Public university, public Land-grant college, land-grant research university with its main campus in Blacksburg, Virginia, United States ...

. Floyd received a PhD in mathematics from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

1978 under the direction of

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

Mathematical contributions

Most of Floyd's research is in the areas of

geometric topology In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topo ...

and

geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these group ...

. Floyd and

Allen Hatcher Allen Edward Hatcher (born October 23, 1944) is an American mathematician specializing in geometric topology. Biography Hatcher was born in Indianapolis, Indiana. After obtaining his Bachelor of Arts, B.A. and Bachelor of Music, B.Mus. from Ober ...

classified all the incompressible

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

s in punctured-

torus In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses inclu ...

bundles over the

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

. In a 1980 paper Floyd introduced a way to compactify a

finitely generated group In algebra, a finitely generated group is a group ''G'' that has some finite generating set ''S'' so that every element of ''G'' can be written as the combination (under the group operation) of finitely many elements of ''S'' and of inverses o ...

by adding to it a boundary which came to be called the Floyd boundary. Floyd also wrote a number of joint papers with James W. Cannon and Walter R. Parry exploring a combinatorial approach to the Cannon conjecture using

finite subdivision rules In mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric fractals. Instead of repeati ...

. 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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, Providence, RI, 2002, ; pp. 63–64

References

External links

*
William Floyd's webpage
Department of Mathematics,

Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American topologists Virginia Tech faculty Princeton University alumni {{US-mathematician-stub