The Johnson homomorphism and the second cohomology of IAn
By Alexandra Pettet. 2005
60 citations recorded by the source corpus.
Let Fn be the free group on n generators. Define IAn to be group of automorphisms of Fn that act trivially on first homology. The Johnson homomorphism in this setting is a map from IAn to its abelian- ization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology of IAn. A descending central series of IAn is given by the subgroups K (i) n which act trivially on Fn/F (i+1) n , the free rank n, degree i nilpotent group. It is a conjecture of Andreadakis that K (i) n is equal to the lower central series of IAn; indeed K (2) n is known to be the commutator subgroup of IAn. We prove that the quotient group K (3) n /IA (3) is finite for all n and trivial for n = 3. We also compute the rank of K (2) n /K (3) n . AMS Classification 20F28, 20J06; 20F14
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d992a4f3f6dc78255b7dc92e19578a8364c23dfb
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Basis-conjugating automorphisms of a free group and associated Lie algebras (2006, methodology): “N Kawazumi [14], T Sakasai [22], T Satoh [23] and A Pettet [21] have given related cohomological information for IAn .”