Math 151c

Virtual properties of 3-manifolds

Winter 2014-15

Time TBA // Place TBA

Course Description | References | Lecture Notes | Handouts

Instructor: Yi Liu, 374 Sloan, yliumath@caltech.edu, Office Hour: by appointment

Announcements

Course Description

Topics: A virtual property of a 3-manifold is a property satisfied by a finite cover of the 3-manifold. Study of such properties is closely related subgroups of the fundamental group and their separability. Virtual properties of 3-manifolds are a hot topic in recent years.

The goal of course is to give an introduction to the Virtual Haken Conjecture. We plan to spend 4 weeks to study 3-manifold topology from the perspective of Thurston's Geometrization, and 3 weeks to study special cube complexes following the work of D. Wise, and the rest 3 weeks to discuss Agol's proof of VHC. The prerequisite of this course is Ma 151a or equivalent familarity with fundamental groups and covering spaces.

References

• Thurston, W. P., The Geometry and Topology of Three-Manifolds, lecture notes, electronic version

• Hatcher, A., Notes on Basic 3-Manifold Topology, notes, electronic version

• Wise, D. T., The Structure of Groups with a Quasiconvex Hierarchy, notes, electronic version

Lecture Notes

Handouts

Homework

 Last update:  Nov 17, 2012 | © California Institute of Technology | Questions?  kaubry @ caltech.edu