The Geometry of the Word Problem for Finitely Generated Groups
The advanced course on The geometry of the word problem for ?nitely presented groups was held July 5–15, 2005, at the Centre de Recerca Matematica ` in B- laterra (Barcelona). It was aimed at young researchersand recent graduates int- ested in geometricapproachesto grouptheory,in particular,to the wordproblem. Three eight-hour lecture series were delivered and are the origin of these notes. There were also problem sessions and eight contributed talks. The course was the closing activity of a research program on The geometry of the word problem, held during the academic year 2004–05 and coordinated by Jos´ eBurilloandEnricVenturafromtheUniversitatPolit` ecnicadeCatalunya,and Noel Brady,fromOklahoma University. Thirty-?vescientists participated in these events, in visits to the CRM of between one week and the whole year. Two weekly seminars and countless informal meetings contributed to a dynamic atmosphere of research. The authors of these notes would like to express their gratitude to the m- velous sta? at the CRM, director Manuel Castellet and all the secretaries, for providing great facilities and a very pleasant working environment. Also, the - thors thank Jos´ e Burillo and Enric Ventura for organising the research year, for ensuring its smooth running, and for the invitations to give lecture series. - nally, thanks are due to all those who attended the courses for their interest, their questions, and their enthusiasm.
Contains accounts of many recent developments in Geometric Group Theory and shows the interaction between the word problem and geometry continues to be a central themeIllustrated with many figures and containing numerous exercises and open questions