Surveys in Differential Geometry (Surveys in Differential Geometry) vol.3 (Surveys in Differential Geometry)

The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community. The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999. The world-renowned Journal of Differential Geometry sponsors a triannual conference at Harvard University which brings together mathematicians from all over the world. The third conference celebrated the 30th anniversary of the journal, and the 70th birthday of its founding editor, C. C. Hsiung. This volume (Vol.3) of Surveys in Differential Geometry is based on the lectures given during the 3rd conference of Journal of Differential Geometry. As a service to the mathematics community, the editors of the Journal of Differential Geometry decided to organize a conference, to be held every three years, at which invited speakers would survey the field of differential geometry and related subjects. In choosing the speakers, the editors look at geometry in a very broad way and hope geometers will go beyond the classical perception of other fields. Among the speakers at the conferences are people working in algebraic geometry, mathematical physics and other fields. The speakers are prominent specialists in their respective areas who are able to give a broad overview of recent trends and to make predictions and suggestions for future research. The editors believe that these conferences are useful gatherings for experts and nonexperts alike, and in particular for those who are isolated from the mainstream of activity in geometry. This volume reflects the first conference, which was held at Harvard University in April 1990. This volume contains papers taken from the third conference held at Harvard University on differential geometry. It includes discussion of local index theory eta invariants, embedded surfaces and gauge theory in three and four dimensions, and Thurston's hyperbolization of Haken manifolds.