Geometry & Topology
- Geom. Topol.
- Volume 19, Number 4 (2015), 2217-2255.
Generating the Johnson filtration
For , let be the term in the Johnson filtration of the mapping class group of a genus surface with one boundary component. We prove that for all , there exists some such that is generated by elements which are supported on subsurfaces whose genus is at most . We also prove similar theorems for the Johnson filtration of and for certain mod- analogues of the Johnson filtrations of both the mapping class group and of . The main tools used in the proofs are the related theories of FI–modules (due to the first author with Ellenberg and Farb) and central stability (due to the second author), both of which concern the representation theory of the symmetric groups over .
Geom. Topol., Volume 19, Number 4 (2015), 2217-2255.
Received: 23 December 2013
Revised: 21 August 2014
Accepted: 3 October 2014
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F05: Generators, relations, and presentations 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Secondary: 57M07: Topological methods in group theory 57N05: Topology of $E^2$ , 2-manifolds
Church, Thomas; Putman, Andrew. Generating the Johnson filtration. Geom. Topol. 19 (2015), no. 4, 2217--2255. doi:10.2140/gt.2015.19.2217. https://projecteuclid.org/euclid.gt/1510858803