The Johnson homomorphism and its kernel

Details The Johnson homomorphism and its kernel The Johnson homomorphism and its kernel

2009-04-02

arxiv.org/abs/0904.0467v2

Mathematics

Geometric Topology

32 pages, 12 figures, a few mistakes corrected

Scientific paper

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general result that also applies to "subsurface Torelli groups". Using this, we extend Johnson's calculation of the rational abelianization of the Torelli group not only to the subsurface Torelli groups, but also to finite-index subgroups of the Torelli group that contain the kernel of the Johnson homomorphism.

Affiliated with

Also associated with

No associations

Rating

The Johnson homomorphism and its kernel does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Johnson homomorphism and its kernel, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Johnson homomorphism and its kernel will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-150162