William Floyd and Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle.

As corollaries, this gave more examples of non-Haken, non-Seifert fibered, irreducible 3-manifolds and extended the techniques and line of investigation started in Thurston's Princeton lecture notes.

In the case of one torus boundary, one can conclude that the number of slopes given by essential surfaces is finite.

He invented the notion of "end-incompressibility" and several of his students, such as Mark Brittenham, Charles Delman, and Rachel Roberts, have made important contributions to the theory.

Hatcher and Thurston exhibited an algorithm to produce a presentation of the mapping class group of a closed, orientable surface.