SECOND ORDER DEHN FUNCTIONS OF SPLIT EXTENSIONS OF THE FORM

ABSTRACT

The purpose of this paper to show the upper and lower bounds of the second order Dehn functions of particular split extensions of the form , where F is the free group of finite rank freely generated by a finite set . To obtain these bounds we use some geometric techniques by constructing the generating spherical pictures of the second homotopy module of the relevant group presentations.

ACKNOWLEDGMENTS

The author like to thank Prof. Steve J. Pride for his help in the writing of this paper and thank the referee for helpful suggestions and comments. This work was supported partially by China State Eduction Ministry SEYTF Fund and Quangdong NSF (2000, 0864).