Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups

Details Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups

2009-10-25

arxiv.org/abs/0910.4777v1

Mathematics

Geometric Topology

34 pages

Scientific paper

We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of once-bounded surface to a finite-rank abelian group. This improves on the author's previous results [Algebr. Geom. Topol. 7 (2007):1297-1326]. To prove the first result, we express the higher Johnson homomorphisms as coboundary maps in group cohomology. Our methods involve the topology of nilpotent homogeneous spaces and lattices in nilpotent Lie algebras. In particular, we develop a notion of the "polynomial straightening" of a singular homology chain in a nilpotent homogeneous space.

Affiliated with

Also associated with

No associations

Rating

Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups 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 Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-561970