圈复形的临界能级和Jacobi场
Critical levels and Jacobi fields in a complex of cycles
摘要：
本文证明了圈复形中连接任意两个顶点的紧测地线段空间具有有限的一致有界维数。的尺寸定义的离散模拟的Jacobi字段，明确构建和示出给一个完整的描述整个空间的紧测地线。雅可比场测量测地稳定性破坏的程度。与大多数曲线复形的有限性不同，这里提出的论点不依赖于双曲性，而是依赖于类似于莫尔斯理论的结构。
英文摘要：
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which are explicitly constructed and shown to give a complete description of the entire space of tight geodesics. Jacobi fields measure the extent to which geodesic stability breaks down. Unlike most finiteness properties of curve complexes, the arguments presented here do not rely on hyperbolicity, but rather on structures similar to Morse theory.
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