Part B Examination of Mr. William Chong

DATE: Wednesday, July 12, 2023

TIME: 3:00 p.m.

PLACE: Zoom online meeting

PRINCIPAL EXAMINERS:

Prof. Daniel Wise

Topic 1: Definitions and examples of the growth of finitely generated groups and their growth series; examples of groups of exponential growth and polynomial growth; the definition of branch groups. References: 1. Topics in Geometric Group Theory. Pierre de la Harpe. Chapters VI to VII (pp. 151 - 209) 2. Branch Groups. Laurent Bartholdi, Rostislav I. Grigorchuk and Zoran Sunik. Chapters 0 to 1 (pp. 1 - 31)

Prof. Piotr Przytycki

Topic 2: Definitions and examples of special cube complexes. Relationship with Right-angled Artin groups and Coxeter groups. Application to Virtually Clean VH-Complexes. Canonical Completion and Retraction of special cube complexes. Separability of Quasiconvex Subgroups and its converse theorem. Linear version of Rips short exact sequence. Cubulation of Coxeter groups. A boundary criterion for cubulation. References: Special Cube Complexes. Frederic Haglund and Daniel T. Wise. Chapters 1 to 8 and 10. Coxeter Groups are Virtually Special. Frederic Haglund and Daniel T. Wise. A Boundary Criterion for Cubulation. Nicolas Bergeron and Daniel T. Wise.

OTHER

EXAMINERS: Anush Tserunyan (Additional Examiner)

Marcin Sabok (Additional Examiner)

Jerome Vetois (Chair, Exam Committee) TBC

The examination is open to staff members and visitors but not to students