scl标准球的面孔
Faces of the scl norm ball
摘要：
设F是S的基本群，其中S是一个紧致的、连通的、有向的、具有负欧拉示性数的非空边界曲面。(1)链\partial S在B_1（F）中的投射类与单位球的余维一个面的内部在稳定交换子长度伪范数下相交。(2)F上与这个面对偶的唯一齐次拟同构（直到H ^1的尺度和元素）是与F在双曲平面的理想边界上的作用相关联的旋转拟同构，它来自S上的一个双曲结构。这些事实来自于这样一个事实，即S中的每一个同调平凡1-链都理性地与一个具有足够大的边界倍数的浸入曲面共界。这是真的，即使S没有边界。
英文摘要：
Let F be the fundamental group of S, where S is a compact, connected, oriented surface with negative Euler characteristic and nonempty boundary. (1) The projective class of the chain \partial S in B_1(F) intersects the interior of a codimension one face of the unit ball in the stable commutator length pseudo-norm. (2) The unique homogeneous quasimorphism on F dual to this face (up to scale and elements of H^1) is the rotation quasimorphism associated to the action of F 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 in S rationally cobounds an immersed surface with a sufficiently large multiple of the boundary. This is true even if S has no boundary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
