Tetrahedra of flags, volume and homology of SL.3/
Tetrahedra of flags, volume and homology of SL.3/
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DOI：
10.2140/gt.2014.18.1911
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发表时间：
2011-01
影响因子：
2
通讯作者：
N. Bergeron;E. Falbel;A. Antonin
中科院分区：
文献类型：
--
作者：
N. Bergeron;E. Falbel;A. Antonin
本文定义了旗形四面体单纯复形的“体积”。这推广和统一了Falbel [6]，Falbel和Wang [8]中所考虑的双曲流形的经典体积和CR四面体复形的体积.我们描述当这个量属于布洛赫组，更一般地描述一个变化公式的边界数据。在此过程中，我们恢复和推广了Neumann和Zagier [18]，Neumann [16]和Kabaya [15]的结果。我们的方法与Fock和Goncharov的工作非常相关[9; 10]。57M50; 57N10，57R20
In the paper we define a “volume” for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrahedral complexes considered in Falbel [6], and Falbel and Wang [8]. We describe when this volume belongs to the Bloch group and more generally describe a variation formula in terms of boundary data. In doing so, we recover and generalize results of Neumann and Zagier [18], Neumann [16] and Kabaya [15]. Our approach is very related to the work of Fock and Goncharov [9; 10]. 57M50; 57N10, 57R20