Calegari, Danny (2009) Faces of the scl norm ball. Geometry and Topology, 13 (3). pp. 1313-1326. ISSN 1465-3060 http://resolver.caltech.edu/CaltechAUTHORS:20090828-095911315
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Let F = π_1(S) where S is a compact, connected, oriented surface with χ(S) < 0 and nonempty boundary. (1) The projective class of the chain ∂S ∈ B^H_1(F) intersects the interior of a codimension one face π_S of the unit ball in the stable commutator length norm on B^H_1(F). (2) The unique homogeneous quasimorphism on F dual to π_S (up to scale and elements of H^1(F)) is the rotation quasimorphism associated to the action of π_1(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.
|Additional Information:||© Copyright 2009 Mathematical Sciences Publishers. Received July 22 2008. Accepted January 17 2009. Published February 13 2009. I would like to thank Marc Burger, Benson Farb, David Fisher, Etienne Ghys, Bill Goldman, Walter Neumann, Cliff Taubes and Anna Wienhard for their comments. I am also very grateful to the anonymous referee for corrections and thoughtful comments. While writing this paper I was partially funded by NSF grant DMS 0707130. Mathematical subject classification: Primary: 20F65, 20J05. Secondary: 20F12, 20F67, 55N35, 57M07.|
|Subject Keywords:||immersion; surface; free group; bounded cohomology; scl; polyhedral norm; rigidity; hyperbolic structure; rotation number|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Joy Painter|
|Deposited On:||14 Sep 2009 17:11|
|Last Modified:||26 Dec 2012 11:16|
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