Geometry & Topology
- Geom. Topol.
- Volume 13, Number 3 (2009), 1313-1336.
Faces of the scl norm ball
Let where is a compact, connected, oriented surface with and nonempty boundary.
(1) The projective class of the chain intersects the interior of a codimension one face of the unit ball in the stable commutator length norm on .
(2) The unique homogeneous quasimorphism on dual to (up to scale and elements of ) is the rotation quasimorphism associated to the action of on the ideal boundary of the hyperbolic plane, coming from a hyperbolic structure on .
These facts follow from the fact that every homologically trivial –chain in rationally cobounds an immersed surface with a sufficiently large multiple of . This is true even if has no boundary.
Geom. Topol., Volume 13, Number 3 (2009), 1313-1336.
Received: 22 July 2008
Revised: 19 January 2009
Accepted: 17 January 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20J05: Homological methods in group theory
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 20F12: Commutator calculus 55N35: Other homology theories 57M07: Topological methods in group theory
Calegari, Danny. Faces of the scl norm ball. Geom. Topol. 13 (2009), no. 3, 1313--1336. doi:10.2140/gt.2009.13.1313. https://projecteuclid.org/euclid.gt/1513800248