Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [47]-48).

Science and Technology Education / M.Sc. (Chemical Education)

Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has algebraic degree 2g. Moreover, the stretch factor \lambda is a special algebraic number, called Salem number. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that d≤g. Our examples also give a new approach to a conjecture of Penner.

Science and Technology Education / M.Sc. (Chemical Education)

Thesis (Ph. D.)--Punjab University, 1992. / Includes bibliographical references (p. 174-181).