*Agol's Virtual Haken Theorem* Winter 2013

### Instructor: Danny Calegari

### Tu Th 1:30-2:50 Eckhart 312

### Description of course:

The goal of this course is to give an exposition of Agol's proof of the Virtual Haken Conjecture
of Waldhausen and the Virtual Fibration Conjecture of Thurston.

### Cancellations:

I will be in Israel from Friday January 11 to Friday January 25 so there will be no classes on January 15, 17, 22, 24.

### Notes from class:

Notes on the proof will be posted online here and updated as we go along.

(Notes last updated June 14, 2013)

### References:

- I. Agol Criteria for virtual fibering
- I. Agol The virtual Haken conjecture (with appendix by Agol-Groves-Manning)
- I. Agol, D. Groves, J. Manning Residual finiteness, QCERF and fillings of hyperbolic groups
- N. Bergeron, D. Wise A boundary criterion for cubulation
- B. Bowditch Relatively hyperbolic groups
- R. Charney An introduction to right-angled Artin groups
- B. Farb Relatively hyperbolic groups
- R. Gitik, M. Mitra, E. Rips, M. Sageev Widths of subgroups
- D. Groves and J. Manning Dehn filling in relatively hyperbolic groups
- F. Haglund Finite index subgroups of graph products
- F. Haglund, D. Wise Special cube complexes
- F. Haglund, D. Wise A combination theorem for special cube complexes
- J. Kahn, V. Markovic Immersing almost geodesic surfaces in a closed hyperbolic three manifold
- D. Osin Peripheral fillings of relatively hyperbolic groups
- M. Sageev Codimension 1 subgroups and splittings of groups
- M. Sageev Ends of group pairs and non-positively curved cube complexes
- P.Scott Subgroups of surface groups are almost geometric
- W. Thurston Three dimensional manifolds, Kleinian groups and hyperbolic geometry
- D. Wise The structure of groups with a quasiconvex hierarchy

### Blog summary of argument: