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2009 Faces of the scl norm ball
Danny Calegari
Geom. Topol. 13(3): 1313-1336 (2009). DOI: 10.2140/gt.2009.13.1313


Let F=π1(S) where S is a compact, connected, oriented surface with χ(S)<0 and nonempty boundary.

(1)  The projective class of the chain SB1H(F) intersects the interior of a codimension one face πS of the unit ball in the stable commutator length norm on B1H(F).

(2)  The unique homogeneous quasimorphism on F dual to πS (up to scale and elements of H1(F)) is the rotation quasimorphism associated to the action of π1(S) on the ideal boundary of the hyperbolic plane, coming from a hyperbolic structure on S.

These facts follow from the fact that every homologically trivial 1–chain C in S rationally cobounds an immersed surface with a sufficiently large multiple of S. This is true even if S has no boundary.


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Danny Calegari. "Faces of the scl norm ball." Geom. Topol. 13 (3) 1313 - 1336, 2009.


Received: 22 July 2008; Revised: 19 January 2009; Accepted: 17 January 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1228.20032
MathSciNet: MR2496047
Digital Object Identifier: 10.2140/gt.2009.13.1313

Primary: 20F65, 20J05
Secondary: 20F12, 20F67, 55N35, 57M07

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.13 • No. 3 • 2009
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