This volume is dedicated to Shigeyuki Morita on the occasion of his 60th birthday. It consists of selected papers on recent trends and results in the study of various groups of diffeomorphisms, including mapping class groups, from the point of view of algebraic and differential topology, as well as dynamical ones involving foliations and symplectic or contact diffeomorphisms.

Most of the authors were invited speakers or participants of the International Symposium on Groups of Diffeomorphisms 2006, which was held at the University of Tokyo (Komaba) in September 2006. The editors believe that the scope of this volume well reflects Morita's mathematical interests and hope this book inspires not only the specialists in these fields but also a wider audience of mathematicians.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

• S. R. Fenley -- Asymptotic geometry of foliations and pseudo-Anosov flows--a survey
• K. Igusa -- Pontrjagin classes and higher torsion of sphere bundles
• T. Kitano and T. Morifuji -- \(L^2\)-torsion invariants and the Magnus representation of the mapping class group
• H.-V. Lê and K. Ono -- Parameterized Gromov-Witten invariants and topology of symplectomorphism groups
• R. C. Penner -- Mapping class actions on surface group completions
• T. Sakasai -- Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class group
• T. Akita -- On mod \(p\) Riemann-Roch formulae for mapping class groups
• J. S. Birman, T. E. Brendle, and N. Broaddus -- Calculating the image of the second Johnson-Morita representation
• J. S. Birman, D. Johnson, and A. Putman -- Symplectic Heegaard splittings and linked abelian groups
• D. Burago, S. Ivanov, and L. Polterovich -- Conjugation-invariant norms on groups of geometric origin
• H. Endo -- A generalization of Chakiris' fibrations
• K. Fujiwara -- Subgroups generated by two pseudo-Anosov elements in a mapping class group. I. Uniform exponential growth
• K. Gomi -- Differential characters and the Steenrod squares
• R. Hain -- Relative weight filtrations on completions of mapping class groups
• Y. Kasahara -- Remarks on the faithfulness of the Jones representations
• N. Kawazumi -- On the stable cohomology algebra of extended mapping class groups for surfaces
• D. Kotschick -- Stable length in stable groups
• Y. Mitsumatsu and E. Vogt -- Foliations and compact leaves on 4-manifolds I. Realization and self-intersection of compact leaves
• S. Morita -- Symplectic automorphism groups of nilpotent quotients of fundamental groups of surfaces
• G. Segal and U. Tillmann -- Mapping configuration spaces to moduli spaces
• M. Suzuki -- New examples of elements in the kernel of the Magnus representation of the Torelli group
• T. Tsuboi -- On the simplicity of the group of contactomorphisms
• T. Tsuboi -- On the uniform perfectness of diffeomorphism groups