William J. Floyd is an American mathematician specializing in topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

. He is currently a professor at Virginia Polytechnic Institute and State University

Virginia Polytechnic Institute and State University

Virginia Polytechnic Institute and State University, popularly known as Virginia Tech , is a public land-grant university with the main campus in Blacksburg, Virginia with other research and educational centers throughout the Commonwealth of Virginia, United States, and internationally.Founded in...

.
Floyd received a PhD in Mathematics from Princeton University

Princeton University

Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

 1978 under the direction of William Thurston

William Thurston

William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...

.

Mathematical contributions

Most of Floyd's research is in the areas of geometric topology

Geometric topology

In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...

 and geometric group theory

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 groups act .Another important...

.

Floyd and Allen Hatcher

Allen Hatcher

Allen Edward Hatcher is an American topologist and also a noted author. His book Algebraic Topology, which is the first in a series, is considered by many to be one of the best introductions to the subject....

 classified all the incompressible surface

Surface

In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

s in punctured-torus

Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...

 bundle

Bundle

Bundle or Bundling may refer to:In marketing:* Product bundling, a marketing strategy that involves offering several products for sale as one combined product...

s over the circle

Circle

A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

.

In a 1980 paper Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary.
Floyd also wrote a number of joint papers with J. W. Cannon

James W. Cannon

James W. Cannon is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He is an Orson Pratt Professor of Mathematics at Brigham Young University.-Biographical data:...

 and W. R. Parry exploring a combinatorial approach to the Cannon conjecture

James W. Cannon

James W. Cannon is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He is an Orson Pratt Professor of Mathematics at Brigham Young University.-Biographical data:...

 which represents one of the few plausible lines of attack of the conjecture.

External links

• William Floyd's webpage, Department of Mathematics, Virginia Polytechnic Institute and State University
  Virginia Polytechnic Institute and State University
  Virginia Polytechnic Institute and State University, popularly known as Virginia Tech , is a public land-grant university with the main campus in Blacksburg, Virginia with other research and educational centers throughout the Commonwealth of Virginia, United States, and internationally.Founded in...