Tropicalization of group representations
Tropicalization of group representations
复制标题
群体表征的热带化
DOI：
10.2140/agt.2008.8.279
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发表时间：
2007
影响因子：
0.7
通讯作者：
D. Alessandrini
中科院分区：
文献类型：
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作者：
D. Alessandrini
本文给出了n维流形M上凸射影结构的参数空间的紧化的边界点的一个解释。这些空间是1.M/在SLnC1.R/中表示的各种特征标的闭半代数子集。边界被构造为这个半代数集的“热带化”。在这里，我们表明，几何解释的点的边界可以构建搜索一个热带类似的行动1.M/上的射影空间。要做到这一点，我们需要构建一个热带射影空间，其中包含许多可逆射影映射。我们通过将SLnC 1的Bruhat-Tits建筑推广到具有真实的满射赋值的非阿基米德域来实现这一点。在nD 1的情况下，这些对象是摩根和沙伦用来描述Teichmuller空间的边界点的真实的树。在一般情况下，它们是具有热带射影空间结构的可收缩度量空间。57M60、57M50、51E24、57N16
In this paper we give an interpretation to the boundary points of the compactification of the parameter space of convex projective structures on an n‐manifold M . These spaces are closed semi-algebraic subsets of the variety of characters of representations of 1.M/ in SLnC1.R/. The boundary was constructed as the “tropicalization” of this semi-algebraic set. Here we show that the geometric interpretation for the points of the boundary can be constructed searching for a tropical analogue to an action of 1.M/ on a projective space. To do this we need to construct a tropical projective space with many invertible projective maps. We achieve this using a generalization of the Bruhat‐Tits buildings for SLnC1 to nonarchimedean fields with real surjective valuation. In the case nD 1 these objects are the real trees used by Morgan and Shalen to describe the boundary points for the Teichmuller spaces. In the general case they are contractible metric spaces with a structure of tropical projective spaces. 57M60, 57M50, 51E24, 57N16