On the Moduli Space of a Spherical Polygonal Linkage

Canadian mathematical bulletin

关键词: Kloosterman sums;    oscillating coefficients;    estimate;   

DOI  :  10.4153/CMB-1999-037-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We give a ``wall-crossing'' formula for computing the topology ofthe moduli space of a closed $n$-gon linkage on $mathbb{S}^2$.We do this by determining the Morse theory of the function$ho_n$ on the moduli space of $n$-gon linkages which is given bythe length of the last side---the length of the last side isallowed to vary, the first $(n - 1)$ side-lengths are fixed. Weobtain a Morse function on the $(n - 2)$-torus with level setsmoduli spaces of $n$-gon linkages. The critical points of $ho_n$are the linkages which are contained in a great circle. We give aformula for the signature of the Hessian of $ho_n$ at such alinkage in terms of the number of back-tracks and the windingnumber. We use our formula to determine the moduli spaces of allregular pentagonal spherical linkages.

【 授权许可】

Unknown