Geometry & Topology Monographs 2 (1999) 349–406

DOI: 10.2140/gtm.1999.2.349

arXiv: math.GT/9911258

Abstract

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between the structure of the mapping class group and invariants of 3–manifolds, the unstable cohomology of the moduli space of curves and Faber’s conjecture, cokernel of the Johnson homomorphisms and the Galois as well as other new obstructions, cohomology of certain infinite dimensional Lie algebra and characteristic classes of outer automorphism groups of free groups and the secondary characteristic classes of surface bundles. We give some experimental results concerning each of them and, partly based on them, we formulate several conjectures and problems.

Keywords

mapping class group, Torelli group, Johnson homomorphism, moduli space of curves

Mathematical Subject Classification

Primary: 32G15, 57R20

Secondary: 14H10, 55R40, 57M99, 57N05

References

Publication

Received: 30 December 1998
Revised: 29 March 1999
Published: 21 November 1999

Authors